Recent zbMATH articles in MSC 76Dhttps://zbmath.org/atom/cc/76D2023-11-13T18:48:18.785376ZWerkzeugSteady-state solutions for the Muskat problemhttps://zbmath.org/1521.340412023-11-13T18:48:18.785376Z"Sánchez, Omar"https://zbmath.org/authors/?q=ai:sanchez.omarIn this paper, the author analyzes the existence of stationary solutions \(z=(z_1,z_2)\) for the Muskat problem with a large surface tension coefficient. Namely, it is considered the unstable case in which the heavier fluid is above the other one and the following initial conditions are imposed:
\[
z(0)=(0,0)\text{ and } z'(0)=(-\alpha,1),\quad\alpha>0.
\]
Assuming the conditions, the solution curve \(z\) can be written as the graph of a function, \(z(y)=(h(y),y))\) where \(h\) solves
\[
-\frac{h''}{(1+h'^2)^{3/2}}+\lambda y=0,\quad h(0)=0,\quad h'(0)=-\alpha.
\]
Then, denoting by \(B\) the beta function, and based on some estimates found in [\textit{M. Ehrnström} et al., Methods Appl. Anal. 20, No. 1, 33--46 (2013; Zbl 1291.34042)], the author is able to prove the existence of a \(\lambda^\ast>0\) such that for all
\[
\lambda\in \left(\lambda^\ast,\tfrac{1}{2\pi^2}B^2(3/4,1/2)\right]
\]
there exists a stationary \(2\pi\)-periodic solution of the Muskat problem that does not self-intersect. Moreover, if \(\lambda<\lambda^\ast\), no periodic solutions can arise. Finally, some numerical experiments are done analyzing the length of the interval \((\lambda^\ast,\frac{1}{2\pi^2}B^2(3/4,1/2))\).
Reviewer: Eduardo Muñoz-Hernández (Madrid)\(\Gamma\)-convergence for nearly incompressible fluidshttps://zbmath.org/1521.351342023-11-13T18:48:18.785376Z"Bella, Peter"https://zbmath.org/authors/?q=ai:bella.peter"Feireisl, Eduard"https://zbmath.org/authors/?q=ai:feireisl.eduard"Oschmann, Florian"https://zbmath.org/authors/?q=ai:oschmann.florianSummary: We consider the time-dependent compressible Navier-Stokes equations in the low Mach number regime in a family of domains \(\Omega_\varepsilon\subset \mathbb{R}^d\) converging in the sense of Mosco to a domain \(\Omega\subset \mathbb{R}^d\), \(d\in\{2, 3\}\). We show the limit is the incompressible Navier-Stokes system in \(\Omega\).
{\copyright 2023 American Institute of Physics}Modification of optimal homotopy asymptotic method for multi-dimensional time-fractional model of Navier-Stokes equationhttps://zbmath.org/1521.351352023-11-13T18:48:18.785376Z"Jan, Himayat Ullah"https://zbmath.org/authors/?q=ai:jan.himayat-ullah"Ullah, Hakeem"https://zbmath.org/authors/?q=ai:ullah.hakeem"Fiza, Mehreen"https://zbmath.org/authors/?q=ai:fiza.mehreen"Khan, Ilyas"https://zbmath.org/authors/?q=ai:khan.ilyas"Mohamed, Abdullah"https://zbmath.org/authors/?q=ai:mohamed.abdullah"Mousa, Abd Allah A."https://zbmath.org/authors/?q=ai:mousa.abd-allah-a(no abstract)On the motion of a large number of small rigid bodies in a viscous incompressible fluidhttps://zbmath.org/1521.351382023-11-13T18:48:18.785376Z"Feireisl, Eduard"https://zbmath.org/authors/?q=ai:feireisl.eduard"Roy, Arnab"https://zbmath.org/authors/?q=ai:roy.arnab"Zarnescu, Arghir"https://zbmath.org/authors/?q=ai:zarnescu.arghir-daniConsider a viscous incompressible fluid within a domain (in \(\mathbb{R}^2\) or \(\mathbb{R}^3\)). Now, let a finite number of rigid bodies be immersed in the fluid, and allow then eventually collide. The purpose of this paper is to better understand and clarify this phenomena under the conditions stated in its introduction.
Reviewer: Igor Leite Freire (São Carlos)Unstable Stokes waveshttps://zbmath.org/1521.351392023-11-13T18:48:18.785376Z"Hur, Vera Mikyoung"https://zbmath.org/authors/?q=ai:hur.vera-mikyoung"Yang, Zhao"https://zbmath.org/authors/?q=ai:yang.zhao.1Summary: We investigate the spectral instability of a \(2\pi /\kappa\) periodic Stokes wave of sufficiently small amplitude, traveling in water of unit depth, under gravity. Numerical evidence suggests instability whenever the unperturbed wave is resonant with its infinitesimal perturbations. This has not been analytically studied except for the Benjamin-Feir instability in the vicinity of the origin of the complex plane. Here we develop a periodic Evans function approach to give an alternative proof of the Benjamin-Feir instability and, also, a first proof of spectral instability away from the origin. Specifically, we prove instability near the origin for \(\kappa >\kappa_1:=1.3627827\dots\), and instability due to resonance of order two so long as an index function is positive. Validated numerics establishes that the index function is indeed positive for some \(\kappa <\kappa_1\), whereby there exists a Stokes wave that is spectrally unstable even though it is insusceptible to the Benjamin-Feir instability. The proofs involve center manifold reduction, Floquet theory, and methods of ordinary and partial differential equations. Numerical evaluation reveals that the index function remains positive unless \(\kappa =1.8494040\dots \). Therefore we conjecture that all Stokes waves of sufficiently small amplitude are spectrally unstable. For the proof of the conjecture, one has to verify that the index function is positive for \(\kappa\) sufficiently small.A new regularity criterion for the 3D incompressible Boussinesq equations in terms of the middle eigenvalue of the strain tensor in the homogeneous Besov spaces with negative indiceshttps://zbmath.org/1521.351402023-11-13T18:48:18.785376Z"Ines, Ben Omrane"https://zbmath.org/authors/?q=ai:ines.ben-omrane"Sadek, Gala"https://zbmath.org/authors/?q=ai:sadek.gala"Ragusa, Maria Alessandra"https://zbmath.org/authors/?q=ai:ragusa.maria-alessandraSummary: This paper is concerned with the logarithmically improved regularity criterion in terms of the middle eigenvalue of the strain tensor to the 3D Boussinesq equations in Besov spaces with negative indices. It is shown that a weak solution is regular on \((0, T]\) provided that
\[
\int_0^T \frac{\| \lambda_2^+ (\cdot, t) \|^{\frac{2}{2-\delta}}_{\dot{B}_{\infty, \infty}^{-\delta}}}{\ln (e + \| u(\cdot, t) \|_{\dot{B}_{\infty,\infty}^{-\delta}}} dt < \infty.
\]
for some \(0< \delta <1\). As a consequence, this result is some improvements of recent works by \textit{J. Neustupa} and \textit{P. Penel} [Adv. Math. Fluid Mech. 237--268, 237--268 (2001; Zbl 1027.35094)] and \textit{E. Miller} [Arch. Ration. Mech. Anal. 235, No. 1, 99--139 (2020; Zbl 1434.35060)].Steady Euler flows on \({\mathbb{R}}^3\) with wild and universal dynamicshttps://zbmath.org/1521.370362023-11-13T18:48:18.785376Z"Berger, Pierre"https://zbmath.org/authors/?q=ai:berger.pierre"Florio, Anna"https://zbmath.org/authors/?q=ai:florio.anna"Peralta-Salas, Daniel"https://zbmath.org/authors/?q=ai:peralta-salas.danielSummary: Understanding complexity in fluid mechanics is a major problem that has attracted the attention of physicists and mathematicians during the last decades. Using the concept of renormalization in dynamics, we show the existence of a locally dense set \({\mathscr{G}}\) of stationary solutions to the Euler equations in \({\mathbb{R}}^3\) such that each vector field \(X\in{\mathscr{G}}\) is universal in the sense that any area preserving diffeomorphism of the disk can be approximated (with arbitrary precision) by the Poincaré map of \(X\) at some transverse section. We remark that this universality is approximate but occurs at all scales. In particular, our results establish that a steady Euler flow may exhibit any conservative finite codimensional dynamical phenomenon; this includes the existence of horseshoes accumulated by elliptic islands, increasing union of horseshoes of Hausdorff dimension 3 or homoclinic tangencies of arbitrarily high multiplicity. The steady solutions we construct are Beltrami fields with sharp decay at infinity. To prove these results we introduce new perturbation methods in the context of Beltrami fields that allow us to import deep techniques from bifurcation theory: the Gonchenko-Shilnikov-Turaev universality theory and the Newhouse and Duarte theorems on the geometry of wild hyperbolic sets. These perturbation methods rely on two tools from linear PDEs: global approximation and Cauchy-Kovalevskaya theorems. These results imply a strong version of V.I. Arnold's vision on the complexity of Beltrami fields in Euclidean space.An optimal control approach to a fluid-structure interaction parameter estimation problem with inequality constraintshttps://zbmath.org/1521.490242023-11-13T18:48:18.785376Z"Chirco, Leonardo"https://zbmath.org/authors/?q=ai:chirco.leonardo"Manservisi, Sandro"https://zbmath.org/authors/?q=ai:manservisi.sandroSummary: In this work, we present a new optimal control approach to fluid-structure interaction parameter estimation problems. The goal is to obtain the desired deformation by controlling the solid material properties, such as the Young modulus. We consider a stationary monolithic FSI problem where solid and liquid forces at the interface are automatically balanced. We consider inequality constraints in order to bound the Young modulus control admissible set. For the optimization, we adopt the Lagrange multiplier method with adjoint variables and obtain the optimality system which minimizes the augmented Lagrangian functional. We implement a projected gradient-based algorithm in a multigrid finite element code suitable for the study of large solid displacements. In order to support the proposed approach, we perform numerical tests with different objectives and control constraints.Invariant measure for 2D stochastic Cahn-Hilliard-Navier-Stokes equationshttps://zbmath.org/1521.600302023-11-13T18:48:18.785376Z"Qiu, Zhaoyang"https://zbmath.org/authors/?q=ai:qiu.zhaoyang"Wang, Huaqiao"https://zbmath.org/authors/?q=ai:wang.huaqiao"Huang, Daiwen"https://zbmath.org/authors/?q=ai:huang.daiwenThis paper focuses on the invariant measure for stochastic Cahn-Hilliard-Navier-Stokes equations in two-dimensional spaces. Applying the Maslowski-Seidler method, the authors establish the existence of invariant measure in state space \(L^2_x\times H^1\) with the weak topology. Furthermore, they prove the existence of global pathwise solutions using the stochastic compactness argument.
This paper is innovative and interesting. It provides important theoretical tools and methods for studying the dynamic behavior of the stochastic Cahn-Hilliard-Navier-Stokes equations.
Reviewer: Guanggan Chen (Chengdu)The method of fundamental solutions for the Stokes flow with the subdomain techniquehttps://zbmath.org/1521.651372023-11-13T18:48:18.785376Z"Rek, Zlatko"https://zbmath.org/authors/?q=ai:rek.zlatko"Šarler, Božidar"https://zbmath.org/authors/?q=ai:sarler.bozidarSummary: The collocation version of the Method of Fundamental Solutions (MFS) with subdomains is introduced in the present work for the solution of the 2D Stokes flow in backward-facing-step geometry, including Dirichlet and Neumann boundary conditions. The motivation for the present work is the inability of the MFS to solve such problems and the problems with slits and cracks due to the discretization of a single domain. The inability stems from the artificial boundary that is difficult or impossible to properly geometrically set in such cases. The solution for such problems is found by splitting such domains into subdomains. The MFS equations for the equilibrium conditions at the collocation points on the interface between the adjacent subdomains are derived for the Stokes equation. A matrix that simultaneously solves the collocation problem on all the subdomains is formed and solved. A sensitivity study of the MFS results is performed by comparing the relative root mean square error with the reference solution obtained by the classical mesh-based finite volume method on a very fine mesh. The subdomain technique is verified by dividing the domain into 2, 3 and 5 subdomains. The velocity, vorticity and pressure compare very well with the reference solution in all three cases while the solution for the single domain approach is outstandingly poor and inappropriate. The paper shows that the proposed subdomain technique maintains the simplicity, true meshless character and accuracy of the MFS for the Stokes flow in cases where the domain topology requires the use of the subdomain technique.Fluid-plate interaction with Kelvin-Voigt damping and bending moment at the interface: well-posedness, spectral analysis, uniform stabilityhttps://zbmath.org/1521.740532023-11-13T18:48:18.785376Z"Mahawattege, Rasika"https://zbmath.org/authors/?q=ai:mahawattege.rasika"Triggiani, Roberto"https://zbmath.org/authors/?q=ai:triggiani.robertoSummary: We consider a fluid-plate interaction model where the two dimensional plate is subject to viscoelastic (strong) damping, as it occurs in some biological systems [\textit{N. Özkaya} et al., Fundamentals of biomechanics-equilibrium, motion, and deformation. New York, NY: Springer (2021)]. The strength of the Kelvin-Voigt damping is measured by a constant \(0 < \rho \leq 1\). Coupling occurs at the interface between the two media, where each component evolves. In this paper, we apply ``low'' physically hinged boundary interface conditions, which involve the bending moment operator for the plate. We prove four main results: (1) analyticity, on the natural energy space, of the corresponding contraction semigroup (and of its adjoint); (2) sharp location of the spectrum of its generator (and similarly of the adjoint generator), neither of which has compact resolvent, and in fact both of which have the point \(\lambda = -\frac{1}{\rho}\) in their respective continuous spectrum; (3) both original generator and its adjoint have the origin \(\lambda = 0\) as a common eigenvalue with a common, explicit, 1-dimensional eigenspace; (4) The subspace of codimension 1 obtained by the original energy space by factoring out the common 1-dimensional eigenspace is invariant under the action of the (here restricted) semigroup (or of its adjoint), and on such subspace both original and adjoint semigroups are uniformly stable.
For the entire collection see [Zbl 1517.47001].N-side cell-based smoothed finite element method for incompressible flow with heat transfer problemshttps://zbmath.org/1521.742232023-11-13T18:48:18.785376Z"Jiang, Chen"https://zbmath.org/authors/?q=ai:jiang.chen.1"Hong, Chen"https://zbmath.org/authors/?q=ai:hong.chen"Wang, Tiantian"https://zbmath.org/authors/?q=ai:wang.tiantian"Zhou, Guo"https://zbmath.org/authors/?q=ai:zhou.guo(no abstract)Comparisons of two representative methods classified as immersed boundary and domain methodshttps://zbmath.org/1521.742592023-11-13T18:48:18.785376Z"Wang, Shuangqiang"https://zbmath.org/authors/?q=ai:wang.shuangqiang"Zhang, Guiyong"https://zbmath.org/authors/?q=ai:zhang.guiyong"Cai, Yunan"https://zbmath.org/authors/?q=ai:cai.yunan"Yan, Boqian"https://zbmath.org/authors/?q=ai:yan.boqian"Tang, Qian"https://zbmath.org/authors/?q=ai:tang.qianSummary: Immersed methods have proven to be powerful numerical measures to simulate intricate fluid-structure interactions using non-conforming meshes. And they can be classified into immersed boundary methods and immersed domain methods based on the utilization of fictitious fluid around the interface or over the entire solid domain. Their performances are compared in light of several common problems for immersed methods, and two representative methods are employed by immersed boundary-lattice Boltzmann method with smoothed point interpolation method (IBLBM-SPIM) and immersed smoothed point interpolation method (IS-PIM). Numerical tests show that IS-PIM allows a fairly independent mesh size for each domain of fluid and solid, and achieves a smooth solid response; IBLBM-SPIM can ensure numerical stability in a large range of density ratio between solid and fluid by setting a proper time step to alleviate the added mass effect, and has a direct influence on the deformation and motion of solids. The present study also gives some enlightening thoughts on developing novel methods to deal with different FSI problems.Simulating fluid-structure interactions with a hybrid immersed smoothed point interpolation methodhttps://zbmath.org/1521.742602023-11-13T18:48:18.785376Z"Wang, Shuangqiang"https://zbmath.org/authors/?q=ai:wang.shuangqiang"Zhang, Guiyong"https://zbmath.org/authors/?q=ai:zhang.guiyong"Yan, Boqian"https://zbmath.org/authors/?q=ai:yan.boqian"Chen, Yuzhen"https://zbmath.org/authors/?q=ai:chen.yuzhen.1|chen.yuzhen.3|chen.yuzhen.2"Zhang, Zhifan"https://zbmath.org/authors/?q=ai:zhang.zhifanSummary: In this paper, a hybrid immersed smoothed point interpolation method (hybrid IS-PIM) is proposed, which employs a hybrid force approach to impose fluid-structure interaction (FSI) force condition. Compared with the original IS-PIM using a complete body force, the hybrid IS-PIM still utilizes the form of body force for pressure term to enhance the stability of numerical algorithm, and the shear force is applied to the boundary to accord with the physical law and the practical situation. Numerical examples have shown that the body force term enables the proposed method to overcome the constraint of mesh size ratio, and the boundary force term has a direct effect on the motion and deformation of solids, which yields more accurate results in comparison with the complete body force applied in the original IS-PIM. Moreover, the equivalence of FSI force in forms of body force and boundary force are also verified straightforwardly using a series of mesh combinations.Dynamics of circular and rectangular jets in crossflowhttps://zbmath.org/1521.760062023-11-13T18:48:18.785376Z"Pokharel, Pranaya"https://zbmath.org/authors/?q=ai:pokharel.pranaya"Acharya, Sumanta"https://zbmath.org/authors/?q=ai:acharya.sumantaSummary: In this work, jets in crossflow (JICFs) were studied numerically through large-eddy simulation using a velocity ratio of 5.7 and a jet Reynolds number of 5000. A parabolic profile was used for the jet inlet and four specific cases were compared: one with a circular inlet and three with rectangular pipe inlets (aspect ratios: 2:1, 0.5:1, and 3:1) having the same mass flow rate of the jet. The results indicated that the rectangular JICFs penetrated the domain more deeply than the circular JICF and delayed the vortex and turbulence breakdown. The effect of the crossflow on the jet orientation was also studied and quantified, and modal analysis was conducted on the cases with dynamic mode decomposition. The significant modes were found to be consistent with spectral analysis of convectively unstable JICFs in the literature. The rectangular JICFs showed increased dominant modes frequencies compared to the circular JICF.Artificial compressibility method using bulk viscosity term for an unsteady incompressible flow simulationhttps://zbmath.org/1521.760262023-11-13T18:48:18.785376Z"Yasuda, T."https://zbmath.org/authors/?q=ai:yasuda.takahiro"Tanno, I."https://zbmath.org/authors/?q=ai:tanno.itaru"Hashimoto, T."https://zbmath.org/authors/?q=ai:hashimoto.tomohisa"Morinishi, K."https://zbmath.org/authors/?q=ai:morinishi.koji"Satofuka, N."https://zbmath.org/authors/?q=ai:satofuka.nobuyukiSummary: We introduced bulk viscosity term into the artificial compressibility method (ACM) for unsteady incompressible flow simulation to improve the efficiency of ACM. The stability, accuracy and computational effort were investigated by changing the Mach number, grid resolution and discretization method to clarify the bulk viscosity effects. ACM with bulk viscosity term (BVACM) could improve the stability and the accuracy of the ACM simulation especially for the coarse grid case. As a result, BVACM was 5.94 times faster than ACM within a permissible error of 5 percent. The three-dimensional flow structure of decaying isotropic turbulence, lid-driven cavity flow, channel flow were efficiently solved by BVACM using parallel computation.Families of superposable planar exact solutions for skew-symmetric couple stress fluid flowshttps://zbmath.org/1521.760322023-11-13T18:48:18.785376Z"Joseph, Subin P."https://zbmath.org/authors/?q=ai:joseph.subin-pSummary: Several types of new planar exact solutions are derived for skew-symmetric couple stress fluid flows. These solutions are obtained by assuming the stream function as a finite sum of constituent functions with different arguments. A large class of spatially periodic new exact solutions are constructed from the first family of solutions. The derived solutions are having complex two-dimensional vortex structures which generalizes the Taylor vortices. All the derived solutions are superposable in such a way that any finite linear combination of the solutions are again exact solutions. Exact solutions for Navier-Stokes equations of motion are also derived as a special case of these flows. Several explicit exact solutions are discussed and illustrated in the paper.Multiple drops impact onto a liquid film: direct numerical simulation and experimental validationhttps://zbmath.org/1521.760412023-11-13T18:48:18.785376Z"Fest-Santini, S."https://zbmath.org/authors/?q=ai:fest-santini.s"Steigerwald, J."https://zbmath.org/authors/?q=ai:steigerwald.j"Santini, M."https://zbmath.org/authors/?q=ai:santini.marina|santini.massimo"Cossali, G. E."https://zbmath.org/authors/?q=ai:cossali.gianpietro-elvio"Weigand, B."https://zbmath.org/authors/?q=ai:weigand.bernhardSummary: A simultaneous impact of three water drops (aligned with equidistant spacing) onto a solid wall covered by a thin liquid film is predicted by direct numerical simulation using the multiphase code Free Surface 3D (FS3D) which is based on the volume-of-fluid (VOF) method and uses the piecewise linear interface calculation (PLIC) method to reconstruct the interface. The numerically reproduced splashing morphology is qualitatively and quantitatively compared with available experimental data and theoretical models. The results show the reliability of the numerical tool (FS3D) to predict quantitatively the complex phenomena involved in detail, like the evolution of crown geometry and the liquid structures resulting from the interaction between the different crowns. The comparison evidenced also the most important critical aspects of the numerical simulation of such complex phenomena, not often reported or even considered in the available open literature (e.g. the early lamella rupture observed in the simulation, caused by a limited numerical resolution, antagonist to the inadequacy of related rupture models). This phenomenon is still a challenging research topic (from both the experimental and the numerical side) and its study is still a necessary step for gaining detailed knowledge for improving the stochastic simulations of multiple drops impact onto liquid films.The dual problem to M. A. Goldshtik problem with arbitrary vorticityhttps://zbmath.org/1521.760452023-11-13T18:48:18.785376Z"Vaĭnshteĭn, Isaak I."https://zbmath.org/authors/?q=ai:vainshtein.isaak-iSummary: The existence of solutions of the dual problem to M. A. Goldshtik problem with arbitrary vorticity was proved in this paper. The effect of non-uniqueness of the solution was determined on a model example.Effect of artificial speed of sound in ACM, EDACM, and EMV for two-dimensional cavity flowhttps://zbmath.org/1521.760492023-11-13T18:48:18.785376Z"Ikegaya, N."https://zbmath.org/authors/?q=ai:ikegaya.naoki"Nagata, K."https://zbmath.org/authors/?q=ai:nagata.kensuke|nagata.kazuhiro|nagata.kuniichi|nagata.kouji|nagata.keitaro|nagata.kenji|nagata.koji|nagata.ken-ichi|nagata.kiyoshi|nagata.koji.1"Hirose, C."https://zbmath.org/authors/?q=ai:hirose.c"Tanimoto, J."https://zbmath.org/authors/?q=ai:tanimoto.junSummary: This study compared various numerical schemes that have been reported with the assumption that artificial compressibility aids in the realization of explicit fluid dynamics simulations for a two-dimensional cavity flow. Four artificial compressible schemes, the artificial compressible method (ACM), entropically dumped ACM (EDACM), explicit method with virtual particles (EMV), were compared with a conventional incompressible scheme (simplified marker and cell, SMAC). The purpose of the comparisons is clarifying the validity of EMV in which the artificial speed of sound can be theoretically determined. In addition, the effect of the artificial speed of sound was investigated for ACM and compared with EMV. Moreover, three conditions of Reynolds numbers, \(Re =100, 1000\), and 5000, were employed. Under steady-state conditions, the velocity and pressure distributions were found to be consistent among the EMV, ACM, EDACM, and SMAC. Further, the comparisons of the horizontal and vertical profiles indicated that these artificial compressible schemes reproduced the velocities using the incompressible scheme at three Reynolds numbers. In contrast, the temporal development of the velocity fields in the three artificial compressible schemes clearly exhibited small fluctuations in the velocity and pressure around the overall trends determined by SMAC. Further, the power spectral densities demonstrated that such fluctuations were due to compression-wave propagations with the artificial speed of sound. Although no clear differences were observed among EMV, ACM, and EDACM at these Reynolds numbers, EMV was determined to be advantageous in terms of theoretically determining the unique value of the artificial speed of sound once the lattice-grid system was fixed, whereas ACM and EDACM require sensitivity studies to select suitable values.Investigation of correlation between vorticity, Q, \( \lambda_{c i}\), \(\lambda_2\), \(\Delta\) and Liutexhttps://zbmath.org/1521.760732023-11-13T18:48:18.785376Z"Yu, Yifei"https://zbmath.org/authors/?q=ai:yu.yifei"Shrestha, Pushpa"https://zbmath.org/authors/?q=ai:shrestha.pushpa"Alvarez, Oscar"https://zbmath.org/authors/?q=ai:alvarez.oscar"Nottage, Charles"https://zbmath.org/authors/?q=ai:nottage.charles"Liu, Chaoqun"https://zbmath.org/authors/?q=ai:liu.chaoqunSummary: For a long time, people hold an idea that vorticity is equivalent to vortex for fluid flow since vorticity represents rotation for rigid body. Nevertheless, many experimental results do not support this opinion. So, several improved methods have been proposed, including Q, \( \lambda_{c i}\), \(\lambda_2\), \(\Delta\) methods and etc, which are all based on the eigenvalues of the velocity gradient tensor. These methods share a common drawback that they are all scalars and, as a result, are unable to locate the swirling axis which is an important information of rotation. To overcome this shortage, Liutex was proposed as a vector indicator of vortex. The direction of Liutex represents the swirling axis and the magnitude of Liutex is defined as twice the angular speed of rotation. After the introduction of Liutex, many experiments and numerical simulations have shown that Liutex can accurately and correctly capture both big and small vortex, which is better than the existing methods. In this paper, the explicit formulae of vorticity, Q, \( \lambda_{c i}\) and \(\Delta\) in terms of Liutex are derived, followed by correlation analysis based on a direct numerical simulation (DNS) result of boundary layer transition and a large eddy simulation (LES) result of supersonic ramp flow with a fully developed turbulent boundary layer. The results show that correlation between vorticity and Liutex is very small and even negative in strong shear regions. Although the correlations of Q, \( \lambda_{c i}\), \(\lambda_2\) and \(\Delta\) are better than vorticity, they are still small in strong shear regions. The expression of relation between vorticity, Q, \( \lambda_{c i}\), \(\Delta\) and Liutex reveals how these methods are contaminated by shear or stretching or both.On motion of a flooded jet of binary mixture in a viscous fluidhttps://zbmath.org/1521.760782023-11-13T18:48:18.785376Z"Andreev, Viktor K."https://zbmath.org/authors/?q=ai:andreev.viktor-konstantinovich"Sobachkina, Natal'ya L."https://zbmath.org/authors/?q=ai:sobachkina.natalya-leonidovnaSummary: The invariant solution to the problem of motion of a flooded jet of binary mixture in a viscous heatconducting fluid is investigated. The motion is induced by longitudinal pressure gradient in a mixture. The problem reduces to solving a conjugate initial-boundary value problem for parabolic equations. Stationary solution of problem is determined and it is shown that this solution is not the limiting one at different pressure gradients values. Using Laplace transformation properties the exact analytical solution was obtained. Some examples of numerical reconstruction of the velocities, temperatures and concentration fields depending on geometric and physical parameters were considered.On the local pressure expansion for the Navier-Stokes equationshttps://zbmath.org/1521.760792023-11-13T18:48:18.785376Z"Bradshaw, Zachary"https://zbmath.org/authors/?q=ai:bradshaw.zachary"Tsai, Tai-Peng"https://zbmath.org/authors/?q=ai:tsai.tai-pengThe authors discuss relations between distributional, mild and Leray solutions to the three-dimensional Navier-Stokes equations via an analysis of the so-called ``local pressure expansion''. This concept, based on delicate properties of BMO solutions of the Poisson equation, leads to a comparison of various local regularity properties of Navier-Stokes equations solution, independent of Lemarié-Rieusset's Littlewood-Paley decomposition of the pressure. Various applications to uniqueness and regularity questions are also discussed.
Reviewer: Piotr Biler (Wrocław)Asymptotic behavior of weak solutions to the inhomogeneous Navier-Stokes equationshttps://zbmath.org/1521.760802023-11-13T18:48:18.785376Z"Han, Pigong"https://zbmath.org/authors/?q=ai:han.pigong"Liu, Chenggang"https://zbmath.org/authors/?q=ai:liu.chenggang"Lei, Keke"https://zbmath.org/authors/?q=ai:lei.keke"Wang, Xuewen"https://zbmath.org/authors/?q=ai:wang.xuewenThe main result is the time decay in the \(L^2\) norm of weak solutions of the nonhomogeneous incompressible Navier-Stokes equations in the whole space \(\mathbb R^n\), \(n=2,3\). The obtained decay rates are optimal since they coincide with the decay rates for the homogeneous equations known for nearly 40 years.
Reviewer: Piotr Biler (Wrocław)On the Euler\(+\)Prandtl expansion for the Navier-Stokes equationshttps://zbmath.org/1521.760812023-11-13T18:48:18.785376Z"Kukavica, Igor"https://zbmath.org/authors/?q=ai:kukavica.igor"Nguyen, Trinh T."https://zbmath.org/authors/?q=ai:nguyen.trinh-t"Vicol, Vlad"https://zbmath.org/authors/?q=ai:vicol.vlad-c"Wang, Fei"https://zbmath.org/authors/?q=ai:wang.fei.2The vanishing viscosity limit for the Navier-Stokes equations in the half-plane supplemented with the Dirichlet boundary condition is studied. The authors justify the validity of the Euler-Prandtl approximation for a class of initial data via vorticity analysis in an \(L^1\)-type norm.
Reviewer: Piotr Biler (Wrocław)Determination of the 3D Navier-Stokes equations with dampinghttps://zbmath.org/1521.760822023-11-13T18:48:18.785376Z"Shi, Wei"https://zbmath.org/authors/?q=ai:shi.wei"Yang, Xinguang"https://zbmath.org/authors/?q=ai:yang.xinguang"Yan, Xingjie"https://zbmath.org/authors/?q=ai:yan.xingjieIn this paper, the authors considered the determination of trajectories for the three-dimensional Navier-Stokes equations with nonlinear damping subject to periodic boundary condition. By making use of the energy estimate of Galerkin approximated equation, the finite number of determining modes and asymptotically determined functionals have been obtained via the Grashof numbers for the non-autonomous and autonomous damped Navier-Stokes fluid flow respectively.
Reviewer: Changxing Miao (Beijing)Density currents front velocity uncertaintyhttps://zbmath.org/1521.760832023-11-13T18:48:18.785376Z"Avila Farenzena, Bruno"https://zbmath.org/authors/?q=ai:avila-farenzena.bruno"Silvestrini, Jorge Hugo"https://zbmath.org/authors/?q=ai:silvestrini.jorge-hugoSummary: Lock-release density currents compose a family of stratified flows that consists of a rapid release of fluid initially confined in an environmental fluid, where the confined fluid usually has a higher density than the environment. When both fluids come into contact, a relative flow is initiated due to buoyancy force variation, configuring a density current. Density currents dynamics can be characterized by observing the temporal evolution of its frontal region position, and propagation velocity, usually referred to as front position and front velocity, respectively. The front position determination is associated with an arbitrary iso-value selection of a scalar field, for example, the density field. The front velocity is normally computed as its time derivative. Since the front position is measured in discrete data, local uncertainties are propagated to the front velocity, thus amplifying the error in its determination. Based in the planar lock-release setup and using numerical simulations as data acquisition method, this study proposes a new method of front position determination free of arbitrary iso-value choice and strategies to minimize local uncertainty errors in the temporal evolution of the front velocity. Obtained results show that the local uncertainty error in front velocity is a function of the spatial discretization, the temporal sampling and the numerical derivative method. Such error can be minimized by the use of interpolation in the front position acquisition method and/or using a new definition for the front velocity proposed in this study.Solving Navier-Stokes with mimetic operatorshttps://zbmath.org/1521.760842023-11-13T18:48:18.785376Z"Brzenski, Jared"https://zbmath.org/authors/?q=ai:brzenski.jared"Castillo, Jose E."https://zbmath.org/authors/?q=ai:castillo.jose-eSummary: We present a new scheme for solving Navier-Stokes equations using mimetic difference operators. These operators can be constructed to high orders of accuracy and maintain the physical properties of the problem under consideration. We demonstrate the effectiveness of our scheme by modeling a lock release in 3D Cartesian coordinates, then extend our techniques to 3D curvilinear grids. The resulting scheme allows for simple and efficient computation of fluid processes on curvilinear grids, which allows us to solve problems in more complex regions while minimizing the restrictions of finite difference methods.A superconsistent collocation method for high Reynolds number flowshttps://zbmath.org/1521.760852023-11-13T18:48:18.785376Z"De l'Isle, François"https://zbmath.org/authors/?q=ai:de-lisle.francois"Owens, Robert G."https://zbmath.org/authors/?q=ai:owens.robert-gSummary: We use a novel implicit second-order projection method together with a superconsistent collocation scheme [\textit{D. Funaro}, SIAM J. Numer. Anal. 30, No. 6, 1664--1676 (1993; Zbl 0796.65120); \textit{L. Fatone} et al., Numer. Methods Partial Differ. Equations 21, No. 4, 649--671 (2005; Zbl 1079.65105); \textit{F. De l'Isle} and \textit{R. G. Owens}, J. Comput. Appl. Math. 391, Article ID 113367, 21 p. (2021; Zbl 1466.65211)] for the solution of the primitive variable formulation of the Navier-Stokes equations at very high Reynolds numbers. In particular, we apply a superconsistent collocation scheme to the convection-diffusion equation arising from one step of the projection method and this represents the first time that superconsistent collocation methods have been employed for the solution of a convection-diffusion equation having unsteady convection velocity. In order to evidence the second-order (in space and time) convergence of our scheme for both the velocity and pressure fields we choose to solve the two-dimensional unsteady Taylor-Green vortex problem [\textit{G. I. Taylor} and \textit{A. E. Green}, Proc. R. Soc. Lond., Ser. A 158, 499--521 (1937; JFM 63.1358.03)]. The numerical results presented for the solution of the two-dimensional square lid-driven cavity problem are in excellent agreement over the whole range of Reynolds numbers considered \((5000 \leq Re \leq 1000)\) with some others in the literature
[\textit{U. Ghia} et al., J. Comput. Phys. 48, 387--411 (1982; Zbl 0511.76031); \textit{T. Wang} and \textit{T. Liu}, Numer. Math., Theory Methods Appl. 12, No. 1, 312--330 (2019; Zbl 1438.65273); \textit{C.-H. Bruneau} and \textit{M. Saad}, Comput. Fluids 35, No. 3, 326--348 (2006; Zbl 1099.76043); \textit{F. Auteri} et al., J. Comput. Phys. 183, No. 1, 1--25 (2002; Zbl 1021.76040); \textit{T. W. Pan} and \textit{R. Glowinski}, ``A projection/wave-like equation method for the numerical simulation of incompressible viscous fluid flow modeled by the Navier-Stokes equations'', Comput. Fluid Dyn. J. 9, 28--42 (2000)].Vorticity-based polynomial adaptation for moving and deforming domainshttps://zbmath.org/1521.760862023-11-13T18:48:18.785376Z"Ghoreishi, Ramin"https://zbmath.org/authors/?q=ai:ghoreishi.ramin"Vermeire, Brian C."https://zbmath.org/authors/?q=ai:vermeire.brian-cSummary: This paper introduces a novel non-dimensional vorticity-based polynomial adaptation indicator for moving and deforming domains using a high-order unstructured spatial discretization. We verify the utility of this approach when applied to the Arbitrary Lagrangian-Eulerian (ALE) form of the compressible Navier-Stokes equations for a range of applications on moving and deforming domains. Specifically, we verify the ALE implementation by performing simulations of an Euler Vortex (EV), and then, illustrate the accuracy and efficiency of the adaptation routine by performing simulations of flow over an oscillating circular cylinder with two different flow settings, dynamic stall of a 2D NACA 0012 airfoil undergoing heaving and pitching motions, shallow dynamic stall of a 3D SD 7003 airfoil undergoing heaving and pitching motions, and flow over a Vertical Axis Wind Turbine (VAWT) composed of two NACA 0012 airfoils. Results demonstrate that the non-dimensional vorticity indicator can track regions of interest, such as vortices and boundary layers, and yields a significant reduction in degrees of freedom when paired with polynomial adaptation.Influence of cylinder breadth and shape on the onset of flow unsteadiness and the aeolian tone levelhttps://zbmath.org/1521.760872023-11-13T18:48:18.785376Z"Gonçalves S. Pinto, Wagner J."https://zbmath.org/authors/?q=ai:goncalves-s-pinto.wagner-j"Margnat, Florent"https://zbmath.org/authors/?q=ai:margnat.florentSummary: The Reynolds number for the onset of flow unsteadiness is determined for several canonical geometries (triangles, rectangles, ellipses and lozenges) at different sectional breadth \((L)\) to height \((d)\) ratios (aspect ratio \(\operatorname{AR} = L \slash d)\), for more than 70 shapes. The flow is modeled using a direct Navier-Stokes incompressible two-dimensional solver and the shape is defined by an Immersed Boundary Method. The employed procedure takes the fluctuation of the velocity in the wake as the criterion to define the unsteadiness and a binary search to find the transition. This procedure yields critical Reynolds number \(\operatorname{Re}_c\) values in agreement with available data in the literature. When \(\operatorname{AR}\) approaches zero, the five shapes lead to almost the same value of 31, which corresponds to \(\operatorname{Re}_c\) for a flat plate normal to the flow. It is then found that \(\operatorname{Re}_c\) grows exponentially with the aspect ratio, the influence of the cross section shape being accounted for by a single regression parameter. For all aspect ratios, the ellipse exhibits the highest \(\operatorname{Re}_c\), and the front-pointing triangle the lowest, the three other geometries laying in between those two. The physics of the influence of cross-section shape on \(\operatorname{Re}_c\) is analyzed, considering its link with recirculation length in particular. An exploitation of the results is outlined for the analysis of recent aeroacoustic shape optimizations at fixed \(\operatorname{Re} = 150\), through correlation between the lift fluctuation at this regime with the distance to the onset of unsteadiness it corresponds to.A hybrid partitioned deep learning methodology for moving interface and fluid-structure interactionhttps://zbmath.org/1521.760882023-11-13T18:48:18.785376Z"Gupta, Rachit"https://zbmath.org/authors/?q=ai:gupta.rachit"Jaiman, Rajeev"https://zbmath.org/authors/?q=ai:jaiman.rajeev-kumarSummary: In this work, we present a hybrid partitioned deep learning framework for the reduced-order modeling of moving interfaces and predicting fluid-structure interaction. Using the discretized Navier-Stokes in the arbitrary Lagrangian-Eulerian reference frame, we generate the full-order flow snapshots and point cloud displacements as target physical data for the learning and inference of coupled fluid-structure dynamics. The hybrid operation of this methodology comes by combining two separate data-driven models for fluid and solid subdomains via deep learning-based reduced-order models (DL-ROMs). The proposed multi-level framework comprises the partitioned data-driven drivers for unsteady flow and the moving point cloud displacements. At the fluid-structure interface, the force information is exchanged synchronously between the two partitioned subdomain solvers. The first component of our proposed framework relies on the proper orthogonal decomposition-based recurrent neural network (POD-RNN) as a DL-ROM procedure to infer the point cloud with a moving interface. This model utilizes the POD basis modes to reduce dimensionality and evolve them in time via long short-term memory-based recurrent neural networks (LSTM-RNNs). The second component employs the convolution-based recurrent autoencoder network (CRAN) as a self-supervised DL-ROM procedure to infer the nonlinear flow dynamics at static Eulerian probes. We introduce these probes as spatially structured query nodes in the moving point cloud to treat the Lagrangian-to-Eulerian conflict together with convenience in training the CRAN driver. To determine these Eulerian probes, we construct a novel snapshot-field transfer and load recovery algorithm. They are chosen in such a way that the two components (i.e., POD-RNN and CRAN) are constrained at the interface to recover the bulk force quantities. These DL-ROM-based data-driven drivers rely on the LSTM-RNNs to evolve the low-dimensional states. A popular prototypical fluid-structure interaction problem of flow past a freely oscillating cylinder is considered to assess the efficacy of the proposed methodology for a different set of reduced velocities that lead to vortex-induced vibrations. The proposed framework tracks the interface description with acceptable accuracy and predicts the nonlinear wake dynamics over the chosen test data range. The proposed framework aligns with the development of partitioned digital twin of engineering systems, especially those involving moving boundaries and fluid-structure interactions.A stabilized local RBF collocation method for incompressible Navier-Stokes equationshttps://zbmath.org/1521.760892023-11-13T18:48:18.785376Z"Jiang, Pengfei"https://zbmath.org/authors/?q=ai:jiang.pengfei"Zheng, Hui"https://zbmath.org/authors/?q=ai:zheng.hui"Xiong, Jingang"https://zbmath.org/authors/?q=ai:xiong.jingang"Zhang, Chuanzeng"https://zbmath.org/authors/?q=ai:zhang.chuanzengSummary: In this work, a stabilized local radial basis function (RBF) collocation method (LRBFCM) is proposed to solve the incompressible Navier-Stokes equations. An improved back ground fictitious grids or meshes technique is proposed to enhance the stability of the LRBFCM. The pressure is computed directly with the coupled velocity field in the Navier-Stokes equations. The explicit time-stepping scheme based on the forward Euler-method is employed for the time discretization, and the free surface of the flow is easy to capture as no numerical integration in the LRBFCM is needed. Numerical results show a high computational speed and a good stability of the proposed LRBFCM.Direct and inverse problems on the joint movement of the three viscous liquids in the flat layershttps://zbmath.org/1521.760902023-11-13T18:48:18.785376Z"Lemeshkova, Elena N."https://zbmath.org/authors/?q=ai:lemeshkova.elena-nikolaevnaSummary: The exact stationary decision of the problem about the joint movement of the three viscous liquids in the flat layers has been found. The decision of the direct and inverse non-stationary problem has been given in the form of the final analytical formulas using the method of Laplas transformation. The following statement has been proved: if a gradient of the pressure in one liquid has a final limit, then the decision is located on a stationary mode. Also for a problem about the ``the flooded layer'' movement it has been shown that velocities converge to the different constants with the time growth.A volume of solid implicit forcing immersed boundary method for solving incompressible Navier-Stokes equations in complex domainhttps://zbmath.org/1521.760912023-11-13T18:48:18.785376Z"Liu, Rex Kuan-Shuo"https://zbmath.org/authors/?q=ai:liu.rex-kuan-shuo"Ng, Khai-Ching"https://zbmath.org/authors/?q=ai:ng.khai-ching"Sheu, Tony Wen-Hann"https://zbmath.org/authors/?q=ai:sheu.tony-wen-hannSummary: In this study, a new implicit forcing immersed boundary (IFIB) method is proposed to solve incompressible viscous fluid flow problems involving complex domains. In the conventional immersed boundary (IB) method, a forcing term computed from the volume of solid (VOS) is added to the incompressible Navier-Stokes equations in order to satisfy the velocity condition within the embedded solid body. However, the velocity boundary condition and the divergence-free condition are enforced at different time levels, i.e. intermediate and new time levels. Penetration of streamlines into the stationary solid body is visible as the velocity boundary condition inside the solid body is not strictly enforced at the new time level. In the current work, the proposed IFIB method can ensure velocity field which satisfies both the velocity boundary condition and the divergence-free condition at the same (new) time level. This is accomplished by solving the pressure equation and calculating the forcing term simultaneously (implicitly). A modified pressure Poisson equation (MPPE) is derived in order to couple the pressure and the forcing terms by treating the forcing term as part of the source term of MPPE. Also, a new cell-based method is proposed to compute the VOS for getting a better parallel efficiency. The accuracy of the present IFIB method is then demonstrated by solving several benchmark problems. No penetration of streamlines has been found in the solid body.Study of the spatial transition in a plane channel flowhttps://zbmath.org/1521.760922023-11-13T18:48:18.785376Z"Machaca Abregu, William I."https://zbmath.org/authors/?q=ai:machaca-abregu.william-i"Dari, Enzo A."https://zbmath.org/authors/?q=ai:dari.enzo-a"Teruel, Federico E."https://zbmath.org/authors/?q=ai:teruel.federico-eSummary: This study presents DNS results of the laminar-turbulent spatial transition in a plane channel flow. The transition is achieved imposing at the inlet the most unstable modes of the associated Orr-Sommerfeld and Squire eigenvalue problems. First, a study of the dependence of the transition on the intensity of the perturbations is presented. For \(Re = 5000\), eleven simulations employing different amplitudes of the Tollmien-Schlichting and oblique waves were analyzed to find that the variation of the friction Reynolds number and shape factor downstream the departure of the transition is roughly independent on the amplitude of the perturbations and that the location of the peak in the friction Reynolds number is strongly dependent on the amplitude of each wave. This implies that, for the type of perturbations simulated here, the transitional phenomenon is essentially delayed or accelerated by the amplitude of the perturbations. Second, two cases with well different amplitude of perturbations are compared in detail. Results show that in both cases the following stages can be identified: quasi-linear stage, late stage, \textit{spike} stage, peak transitional zone, post-transitional zone and fully turbulent zone. Moreover, downstream the first state of the \textit{spike} stage, both cases are essentially equal despite the fact that both transitions are separated by 50 channel half-height diameters in the streamwise coordinate. Finally, the physical phenomenon of the peak zone in the friction Reynolds number is explained considering the coherent vortices packet found across the height of the channel in the super-late stage of the transition.On maximum enstrophy dissipation in 2D Navier-Stokes flows in the limit of vanishing viscosityhttps://zbmath.org/1521.760932023-11-13T18:48:18.785376Z"Matharu, Pritpal"https://zbmath.org/authors/?q=ai:matharu.pritpal"Protas, Bartosz"https://zbmath.org/authors/?q=ai:protas.bartosz"Yoneda, Tsuyoshi"https://zbmath.org/authors/?q=ai:yoneda.tsuyoshiSummary: We consider enstrophy dissipation in two-dimensional (2D) Navier-Stokes flows and focus on how this quantity behaves in the limit of vanishing viscosity. After recalling a number of a priori estimates providing lower and upper bounds on this quantity, we state an optimization problem aimed at probing the sharpness of these estimates as functions of viscosity. More precisely, solutions of this problem are the initial conditions with fixed palinstrophy and possessing the property that the resulting 2D Navier-Stokes flows locally maximize the enstrophy dissipation over a given time window. This problem is solved numerically with an adjoint-based gradient ascent method and solutions obtained for a broad range of viscosities and lengths of the time window reveal the presence of multiple branches of local maximizers, each associated with a distinct mechanism for the amplification of palinstrophy. The dependence of the maximum enstrophy dissipation on viscosity is shown to be in quantitative agreement with the estimate due to [\textit{G. Ciampa} et al., Arch. Ration. Mech. Anal. 240, No. 1, 295--326 (2021; Zbl 1462.35264)], demonstrating the sharpness of this bound.On the initial-boundary problem for thermocapillary motion of an emulsion in spacehttps://zbmath.org/1521.760942023-11-13T18:48:18.785376Z"Petrova, Anna G."https://zbmath.org/authors/?q=ai:petrova.anna-georgevnaSummary: The paper is devoted to the study of the initial-boundary problem for thermocapillary motion of an emulsion in closed bounded domain with sufficiently smooth boundary in the absence of gravity. With the use of Tikhonov-Shauder fixed point theorem the local in time solvability to the problem with zero mean volume velocity of the mixture and zero heat flux on the boundary is proved.DNS of buoyancy-driven flows using EDAC formulation solved by high-order methodhttps://zbmath.org/1521.760952023-11-13T18:48:18.785376Z"Sharma, Manjul"https://zbmath.org/authors/?q=ai:sharma.manjul"Srikanth, Kasturi"https://zbmath.org/authors/?q=ai:srikanth.kasturi"Jayachandran, T."https://zbmath.org/authors/?q=ai:jayachandran.toke"Sameen, A."https://zbmath.org/authors/?q=ai:sameen.aSummary: Entropically Damped Artificial Compressibility (EDAC) equation-based solution method is investigated to simulate the incompressible Navier-Stokes equations for buoyancy-driven flows. The method introduces an evolution equation for pressure, which is used to close the system of equations. The resulting parabolic system removes the need to solve the traditional Poisson's equation at each time step. The energy equation with the Boussinesq approximation and the EDAC system of equations with the low Mach number approximation is solved for the thermal convection problem. This system is discretized using a sixth-order compact difference in space and advanced in time using an explicit fourth-order Runge-Kutta scheme. To investigate the suitability of the EDAC model for buoyancy flows, two widely used benchmark problems, namely: thermal cavity and Rayleigh-Bénard problems, are simulated. The simulation results are compared against the literature data. An excellent agreement is obtained, showing the feasibility and accuracy of the EDAC method in simulating buoyancy-driven flows. The EDAC pressure equation derived from entropy balance, together with the energy equation, are shown in this paper to model thermally dominant flows accurately.A fast, decomposed pressure correction method for an intrusive stochastic multiphase flow solverhttps://zbmath.org/1521.760962023-11-13T18:48:18.785376Z"Turnquist, Brian"https://zbmath.org/authors/?q=ai:turnquist.brian-p"Owkes, Mark"https://zbmath.org/authors/?q=ai:owkes.markSummary: Solution of the pressure Poisson equation is often the most expensive aspect of solving the incompressible form of Navier-Stokes. For a single phase deterministic model the pressure calculation is costly. Expanded to an intrusive stochastic multiphase framework, the simulation expense grows dramatically due to coupling between the stochastic pressure field and stochastic density. To address this issue in a deterministic framework, \textit{M. S. Dodd} and \textit{A. Ferrante} [J. Comput. Phys. 273, 416--434 (2014; Zbl 1351.76161)] discuss a decomposed pressure correction method which utilizes an estimated pressure field and constant density to modify the standard pressure correction method. The resulting method is useful for improving computational cost for one-fluid formulations of multiphase flow calculations. In this paper, we extend the decomposed pressure correction method to intrusive uncertainty quantification of multiphase flows. The work improves upon the original formulation by modifying the estimated pressure field. The new method is assessed in terms of accuracy and reduction in computational cost with oscillating droplet, damped surface wave, and atomizing jet test cases where we find convergence of results with the proposed method to those of a traditional pressure correction method and analytic solutions, where appropriate.A supervised neural network for drag prediction of arbitrary 2D shapes in laminar flows at low Reynolds numberhttps://zbmath.org/1521.760972023-11-13T18:48:18.785376Z"Viquerat, Jonathan"https://zbmath.org/authors/?q=ai:viquerat.jonathan"Hachem, Elie"https://zbmath.org/authors/?q=ai:hachem.elieSummary: Despite the significant breakthrough of neural networks in the last few years, their spreading in the field of computational fluid dynamics is very recent, and many applications remain to explore. In this paper, we explore the drag prediction capabilities of convolutional neural networks for laminar, low-Reynolds number flows past arbitrary 2D shapes. A set of random shapes exhibiting a rich variety of geometrical features is built using Bézier curves. The efficient labelling of the shapes is provided using an immersed method to solve a unified Eulerian formulation of the Navier-Stokes equation. The network is then trained and optimized on the obtained dataset, and its predictive efficiency assessed on several real-life shapes, including NACA airfoils.On the free surface boundary of moving particle semi-implicit method for thermocapillary flowhttps://zbmath.org/1521.760982023-11-13T18:48:18.785376Z"Wang, Zidi"https://zbmath.org/authors/?q=ai:wang.zidi"Sugiyama, Tomoyuki"https://zbmath.org/authors/?q=ai:sugiyama.tomoyuki(no abstract)Geodesic motion on groups of diffeomorphisms with \(H^1\) metric as geometric generalised Lagrangian mean theoryhttps://zbmath.org/1521.760992023-11-13T18:48:18.785376Z"Oliver, M."https://zbmath.org/authors/?q=ai:oliver.marcel"Vasylkevych, S."https://zbmath.org/authors/?q=ai:vasylkevych.sergiySummary: Generalized Lagrangian mean theories are used to analyse the interactions between mean flows and fluctuations, where the decomposition is based on a Lagrangian description of the flow. A systematic geometric framework was recently developed by Gilbert and Vanneste who cast the decomposition in terms of intrinsic operations on the group of volume preserving diffeomorphisms or on the full diffeomorphism group. In this setting, the mean of an ensemble of maps can be defined as the Riemannian centre of mass on either of these groups. We apply this decomposition in the context of Lagrangian averaging where equations of motion for the mean flow arise via a variational principle from a mean Lagrangian, obtained from the kinetic energy Lagrangian of ideal fluid flow via a small amplitude expansion for the fluctuations. We show that the Euler-\(\alpha\) equations arise as Lagrangian averaged Euler equations when using the \(L^2\)-geodesic mean on the volume preserving diffeomorphism group of a manifold without boundaries, imposing a ``Taylor hypothesis'', which states that first order fluctuations are transported as a vector field by the mean flow, and assuming that fluctuations are statistically nearly isotropic. Similarly, the EPDiff equations arise as the Lagrangian averaged Burgers' equations using the same argument on the full diffeomorphism group. A serious drawback of this construction is that the assumptions of Lie transport of the fluctuation vector field and isotropy of fluctuations cannot persist except for an asymptotically vanishing interval of time. To remedy the problem of persistence of isotropy, we suggest adding strong mean-reverting stochastic term to the Taylor hypothesis and identify a scaling regime in which the inclusion of the stochastic term leads to the same averaged equations up to a constant.CFD analysis of a ringless piston's secondary motion and the validity of Reynolds equationhttps://zbmath.org/1521.761002023-11-13T18:48:18.785376Z"Cohen, Igal"https://zbmath.org/authors/?q=ai:cohen.igal"Kligerman, Yuri"https://zbmath.org/authors/?q=ai:kligerman.yuri"Goltsberg, Roman"https://zbmath.org/authors/?q=ai:goltsberg.romanSummary: In the present study the validity of Reynolds equation for the lubrication flow within a ringless piston-cylinder system, with dynamic effects, is considered. The secondary motion, due to perturbations, of a stepped profiled piston is investigated to assess its dynamic response and stability. A variety of problems with different geometries and operating conditions are solved, for different initial conditions, using both Reynolds equation and Navier-Stokes based model. To examine the validity of Reynolds equation, normalized parameters were established. Two dimensionless parameters were considered -- the reduced Reynolds number, \(\mathrm{Re}^\ast\) and the unsteady Reynolds number, \(\mathrm{S}\cdot\mathrm{Re}^\ast\). The discussion is separated to the steady state solution and the initial transient response. Generally, it is found that the stability of the steady solution acquired by Reynolds equation is valid even for higher values of the reduced Reynolds number, \(\mathrm{Re}^\ast\) (up to 2) which includes most of hydrodynamic lubrication applications and it is not affected by the unsteady Reynolds number, \(\mathrm{S}\cdot\mathrm{Re}^\ast\). For unstable steady solution, the unsteady Reynolds number, \(\mathrm{S} \cdot\mathrm{Re}^\ast\), may affect the validity of Reynolds equation. For the transient response, it was found that the Reynolds equation is not valid for \(\mathrm{S}\cdot\mathrm{Re}^\ast > 0.05\), since its solution is over damped, compared to the Navier-Stokes based model. Therefore, using Reynolds equation might lead to a failure in detection of a collision between the vibrating piston and the cylinder.Three-dimensional buoyant hydraulic fractures: constant release from a point sourcehttps://zbmath.org/1521.761012023-11-13T18:48:18.785376Z"Möri, Andreas"https://zbmath.org/authors/?q=ai:mori.andreas"Lecampion, Brice"https://zbmath.org/authors/?q=ai:lecampion.briceSummary: Hydraulic fractures propagating at depth are subjected to buoyant forces caused by the density contrast between fluid and solid. This paper is concerned with the analysis of the transition from an initially radial fracture towards an elongated buoyant growth -- a critical topic for understanding the extent of vertical hydraulic fractures in the upper Earth crust. Using fully coupled numerical simulations and scaling arguments, we show that a single dimensionless number governs buoyant hydraulic fracture growth, namely the dimensionless viscosity of a radial hydraulic fracture at the time when buoyancy becomes of order 1. It quantifies whether the transition to buoyancy occurs when the growth of the radial hydraulic fracture is either still in the regime dominated by viscous flow dissipation or already in the regime where fracture energy dissipation dominates. A family of fracture shapes emerge at late time from finger-like (toughness regime) to inverted elongated cudgel-like (viscous regime). Three-dimensional toughness-dominated buoyant fractures exhibit a finger-like shape with a constant-volume toughness-dominated head and a viscous tail having a constant uniform horizontal breadth: there is no further horizontal growth past the onset of buoyancy. However, if the transition to buoyancy occurs while in the viscosity-dominated regime, both vertical and horizontal growths continue to match scaling arguments. As soon as the fracture toughness is not strictly zero, horizontal growth stops when the dimensionless horizontal toughness becomes of order 1. The horizontal breadth follows the predicted scaling.Machine learning calculation model for hydrodynamic lubrication characteristics of a miter gate bottom pivothttps://zbmath.org/1521.761022023-11-13T18:48:18.785376Z"Xu, Xiang"https://zbmath.org/authors/?q=ai:xu.xiang.1"Guan, Zhengguo"https://zbmath.org/authors/?q=ai:guan.zhengguo"Li, Zhixiong"https://zbmath.org/authors/?q=ai:li.zhixiong"Sulowicz, Maciej"https://zbmath.org/authors/?q=ai:sulowicz.maciej"Królczyk, Grzegorz"https://zbmath.org/authors/?q=ai:krolczyk.grzegorz"Dai, Tiancan"https://zbmath.org/authors/?q=ai:dai.tiancan"Zhao, Xinze"https://zbmath.org/authors/?q=ai:zhao.xinze(no abstract)Synthesis on the existence/non-existence of multiple solutions for an unsteady non-rotating shrinking disk flowhttps://zbmath.org/1521.761032023-11-13T18:48:18.785376Z"Mehmood, A."https://zbmath.org/authors/?q=ai:mehmood.ahmer"Tabassum, G. D."https://zbmath.org/authors/?q=ai:tabassum.ghulam-dastgir"Usman, M."https://zbmath.org/authors/?q=ai:usman.muhammad.1|usman.mustofa|usman.muhammad|usman.murat|usman.mahamood|usman.mohammad"Dar, A."https://zbmath.org/authors/?q=ai:dar.amanullahSummary: Results of studying the problem of an unsteady fluid flow along an instantaneously stretching (shrinking) non-rotating disk with an infinite radius are reported. The velocity of the shrinking disk surface is chosen in such a way that the problem allows the existence of an exact similarity solution. The original problem is reduced to an initial-value problem, which is solved numerically by using the shooting and Newton-Raphson methods. A detailed study of the existence and uniqueness of the solution is performed.Vortex collision against static and spinning round cylinders: a lattice Boltzmann studyhttps://zbmath.org/1521.761042023-11-13T18:48:18.785376Z"De Rosis, Alessandro"https://zbmath.org/authors/?q=ai:de-rosis.alessandroSummary: In this paper, the flow physics generated by the collision of a vortex dipole that moves against a spinning round cylinder is investigated numerically. Fluid dynamics is predicted by a combined central-moments-based lattice Boltzmann-immersed boundary method. First, the model is validated against well established consolidated benchmark problems, showing very high accuracy properties. Then, results from a comprehensive numerical campaign are presented. A wide set of values of the Reynolds number \((\mathrm{Re})\) is investigated, ranging from 10 to 1000. The cylinder is forced to spin around its centre with different angular velocities, which are obtained by varying the spinning number \((\mathrm{Sp})\) between 0 (corresponding to the static case) and 0.75. The generation of secondary vortices as a consequence of the impact is elucidated and linked to the time evolution of the kinetic energy, enstrophy and hydrodynamic forces. Interestingly, we find that the flow physics changes drastically when \(\mathrm{Re} \geq 250\), independently from the value of \(\mathrm{Sp}\). Through a closer look at the vorticity field, we find that the impact creates two primary-secondary structures and a second impingement takes place when \(\mathrm{Re} \geq 250\). Interestingly, the normalised drag force \((C_d)\) is found to constantly fluctuates around a mean value. Oscillations are due to the vorticity created by the rotation of the cylinder and are more emphasised as \(\mathrm{Sp}\) grows. Specifically, \(C_d\) can achieve marked negative values as a consequence of the velocity field created by the cylinder during its rotation.Correlation between vorticity, Liutex and shear in boundary layer transitionhttps://zbmath.org/1521.761052023-11-13T18:48:18.785376Z"Dong, Xiangrui"https://zbmath.org/authors/?q=ai:dong.xiangrui"Hao, Chunyang"https://zbmath.org/authors/?q=ai:hao.chunyang"Liu, Chaoqun"https://zbmath.org/authors/?q=ai:liu.chaoqunSummary: Correlation analysis on the vorticity, Liutex and the anti-symmetric shear, is discussed in this paper based on the new introduced vortex definition of Liutex, to explore the mechanism of the vortex generation in laminar flow transition and the relation between the fluctuation and the rotation. Compared with the volume vorticity as a good measurement to evaluate the statistical fluctuations, a new concept named volume Liutex is introduced in this study to predict the turbulence, which is an accurate yardstick to quantitatively evaluate the degree of the transition from laminar flow to turbulence. A relatively high correlation between the fluctuation and the rotation is discovered in the transitional flow. It is found that the laminar flow transition must be promoted by transforming the anti-symmetric shear to the rotation; the fluctuation of the flow in transition is mainly caused by the flow rotation, or, the turbulence is caused by Liutex generation and growth. In addition, the Reynolds stress is found concentrated in the surrounding area of the vortex core which has a high Liutex value inside.An exact steadily rotating surface quasi-geostrophic elliptical vortexhttps://zbmath.org/1521.761062023-11-13T18:48:18.785376Z"Dritschel, David G."https://zbmath.org/authors/?q=ai:dritschel.david-gSummary: An elliptical region having a particular distribution of anomalous buoyancy or temperature at the surface of an otherwise unbounded rotating stratified fluid is shown to steadily rotate under the quasi-geostrophic approximation. The particular distribution is proportional to the vertical thickness of an ellipsoid, divided by its mean thickness, in the limit of vanishing thickness. The steady rotation of this structure or vortex is assured by the known steady rotation of any ellipsoid, and can be obtained by an appropriate limit. It is found by numerical experimentation that this vortex is stable if its minor to major aspect ratio \(\lambda\) exceeds 0.427, approximately. Notably, a two-dimensional elliptical vortex (having uniform vorticity) is stable for \(\lambda > 1/3\). Instabilities of surface vortices are characterised by the ejection of a weak tongue of buoyancy, which subsequently rolls up into a street of weak vortices. The main vortex is thereby reduced in aspect ratio and remains robust for long times.On the numerical simulation of a confined cavitating tip leakage vortex under geometrical and operational uncertaintieshttps://zbmath.org/1521.761072023-11-13T18:48:18.785376Z"Karimi, Mohamad Sadeq"https://zbmath.org/authors/?q=ai:karimi.mohamad-sadeq"Raisee, Mehrdad"https://zbmath.org/authors/?q=ai:raisee.mehrdad"Farhat, Mohamed"https://zbmath.org/authors/?q=ai:farhat.mohamed"Hendrick, Patrick"https://zbmath.org/authors/?q=ai:hendrick.patrick"Nourbakhsh, Ahmad"https://zbmath.org/authors/?q=ai:nourbakhsh.ahmadSummary: The effects of operational and geometrical uncertainties on Tip Leakage Vortex (TLV) characteristics are investigated in the current research. Geometrical uncertainties are comprised of manufacturing tolerances or gradual geometry degradation over the time modeled by the Karhunen-Loève (KL) expansion. Operational uncertainties include randomness in operating temperature, inlet velocity, and pressure. These stochastic parameters are assumed to have a Beta probability distribution function with a standard deviation equal to measurement error. To perform Uncertainty Quantification (UQ) analysis, the non-intrusive polynomial chaos expansion is utilized. Moreover, Sobol' indices obtain the contribution of each stochastic parameter on the quantity of interest. For numerical simulation of cavitating flow, the SST \(k - \omega\) turbulence model and the Zwart mass transfer model were employed. It was observed that the cavitating tip leakage vortex flow as well as the lift and drag coefficients are profoundly affected by geometrical and operational uncertainties, which can also describe the discrepancies between numerical and experimental results. For instance, the deviation of vortices circulation, vortex core streamwise velocity, lift, and drag coefficients are more than 25\%, 30\%, 40\%, and 70\% of their mean value, respectively. Furthermore, results showed that the characteristics of TLV, like circulation and velocity field, are mostly influenced by operational uncertainties, while the vortex core position and viscous core radius are affected by geometrical randomness, specifically gap distance.Two- and three-dimensional simulations of flow and heat transfer around rectangular cylindershttps://zbmath.org/1521.761082023-11-13T18:48:18.785376Z"Mashhadi, A."https://zbmath.org/authors/?q=ai:mashhadi.a"Sohankar, A."https://zbmath.org/authors/?q=ai:sohankar.ahmadSummary: This numerical study investigates the forced convection heat transfer from and flow topology around isothermal rectangular cylinders. The effects of various cross-sectional aspect ratios (\(AR=0.25-4\)), Reynolds numbers \((Re = 30-200)\), and Prandtl numbers \((Pr = 0.7, 5)\) are examined on the results. Two or three-dimensional simulations are conducted depending on the \(Re\) and \(AR\) employed. The results show that the near primary vortices (Kármán wake) undergo a downstream transition to the two-layered vortices, followed by a transition from the two-layered vortices to the secondary vortices for \(AR \leq 1\). For smaller aspect ratios, the prevailing of the secondary vortices is further accelerated, i.e., they emerge at a lower \(Re\) and a shorter downstream distance from the cylinder. Three types of secondary vortices distinguished based on their shape, strength, and generation mechanism were observed. A geometric criterion (spacing ratio) for the onset of evolution of the two-layer structure is proposed for each \(AR\). It is observed that the sensitiveness of the Nusselt number to \(AR\) and \(Re\) can be ascribed to the change in the scenarios of the flow separation and reattachment (flow regimes), vortex strength, and wake-recirculation size \((L_r)\). The Nusselt number grows with increasing \(Re\) and \(Pr\) but diminishes with \(AR\). The relationship between the average Nusselt number and \(L_r\) is direct in the steady flow, while they are inversely linked in the two- and three-dimensional unsteady flow. Reducing \(AR\) from 4 to 0.25, depending on \(Re\) and \(Pr\), leads to a 90\%--170\% enhancement in the Nusselt number, whereas increasing \(AR\) amplifies the total heat transfer due to an enlargement in the heat transfer surfaces. The second law of thermodynamics analysis reveals that cylinders with smaller \(AR\) generate lower entropy (destroy lower exergy); therefore, they are more efficient.The dynamics of the tip and hub vortices shed by a propeller: Eulerian and Lagrangian approacheshttps://zbmath.org/1521.761092023-11-13T18:48:18.785376Z"Posa, Antonio"https://zbmath.org/authors/?q=ai:posa.antonio"Broglia, Riccardo"https://zbmath.org/authors/?q=ai:broglia.riccardo"Balaras, Elias"https://zbmath.org/authors/?q=ai:balaras.eliasSummary: Large Eddy Simulation on a grid composed of 3.8 billion points is utilized to reproduce the wake of a marine propeller. Results are compared against Particle Imaging Velocimetry experiments. The study is based on a core analysis for the tip and hub vortices, using both Eulerian and Lagrangian methodologies. Results show that the instability of the tip vortices is first triggered by their shear with the wake of the neighboring blades. This promotes short- and long-wave oscillations of the trajectory of the tip vortices and eventually mutual inductance phenomena between them. Then, the process of instability and break-up of the coherence of the tip vortices is accelerated by the interaction with the hub vortex, which is the largest coherent structure shed by the propeller, dominating its wake system and expanding radially as the wake develops downstream. The break-up of the helical structures shed from the tip of the propeller blades results in a substantial increase of turbulence at the wake outer boundary and especially in its diffusion. This process is even enhanced by the energy provided by the hub vortex, associated with its fluctuations at low frequencies. The instability process of the hub vortex is slower than the one experienced by the tip vortices. Although the former develops growing fluctuations around the wake axis, it keeps coherent further downstream, in comparison with the latter. Therefore, within a few diameters from the propeller plane, turbulence at the wake axis keeps decreasing downstream of the onset of the hub vortex.Multi-fidelity vortex simulations of rotor flows: validation against detailed wake measurementshttps://zbmath.org/1521.761102023-11-13T18:48:18.785376Z"Ramos-García, Néstor"https://zbmath.org/authors/?q=ai:ramos-garcia.nestor"Abraham, Aliza"https://zbmath.org/authors/?q=ai:abraham.aliza"Leweke, Thomas"https://zbmath.org/authors/?q=ai:leweke.thomas"Sørensen, Jens Nørkær"https://zbmath.org/authors/?q=ai:sorensen.jens-norkaerSummary: Two flow models with different fidelity of the DTU vortex solver \textbf{MIRAS} have been used to simulate the wake generated by a model wind turbine with various levels of asymmetry. Predictions are validated against experimental Particle Image Velocimetry measurements and dye visualizations. The experiments were conducted in a recirculating free-surface water channel with an immersed two-bladed rotor mounted on a shaft. The blades were designed to approximate a Joukowsky rotor. A detailed comparison between the measurements and the simulations is first performed for an unperturbed baseline case at different tip speed ratios. The analysis consists of a tip vortex characterization, including the vortex core profile, and a comparison of the instantaneous and mean velocity and vorticity fields, along with the mean wake profile at different downstream locations. Overall, good agreement is obtained between measurements and simulations, especially with the higher-fidelity particle-mesh model, which is capable of very closely predicting many of the flow features observed in the experiments. Rotor asymmetry triggers a vortex instability, commonly known as leapfrogging, which accelerates the breakdown of tip vortices, enhancing the mixing of wake structures and promoting a faster wake recovery. The prediction accuracy of this instability by the solvers is analyzed for different tip speed ratios and perturbation amplitudes. This work aims at setting the groundwork for future flow instability studies with the \textbf{MIRAS} solver.Effect of topology changes on the breakup of a periodic liquid jethttps://zbmath.org/1521.761112023-11-13T18:48:18.785376Z"Afanador, Alberto Roman"https://zbmath.org/authors/?q=ai:afanador.alberto-roman"Zaleski, Stéphane"https://zbmath.org/authors/?q=ai:zaleski.stephane"Tryggvason, Gretar"https://zbmath.org/authors/?q=ai:tryggvason.gretar"Lu, Jiacai"https://zbmath.org/authors/?q=ai:lu.jiacaiSummary: The breakup of a periodic jet is examined computationally, using a front-tracking/finite-volume method, where the interface is represented by connected marker points moving with the fluid, while the governing equations are solved on a fixed grid. Tracking the interface allows control of whether topology changes take place or not. The Reynolds and Capillary numbers are kept relatively low \(( R e = 150\) and \(C a = 2)\) so most of the flow is well resolved. The effect of topology changes is examined by following the jet until it has mostly disintegrated, for different ``coalescence criterion,'' based on the thickness of thin films and threads. The evolution of both two-dimensional and fully three-dimensional flows is examined. It is found that although there is a significant difference between the evolution when no breakup takes place and when it does, once breakup takes place the evolution is relatively insensitive to exactly how it is triggered for a range of coalescence criterion, and any differences are mostly confined to the smallest scales.Unsteady vortex shedding dynamics behind a circular cylinder in very shallow free-surface flowshttps://zbmath.org/1521.761122023-11-13T18:48:18.785376Z"Alzabari, Fawaz"https://zbmath.org/authors/?q=ai:alzabari.fawaz"Wilson, Catherine A. M. E."https://zbmath.org/authors/?q=ai:wilson.catherine-a-m-e"Ouro, Pablo"https://zbmath.org/authors/?q=ai:ouro.pabloSummary: The turbulent wake generated by a horizontal circular cylinder in free-surface flows of increasing shallowness with submergence-to-diameter ratios between 0.5 and 2.1 are investigated using large-eddy simulation. At Froude number \((Fr) = 0.26\), the free-surface deformation is small with little influence on the wake, whereas at \(Fr = 0.53\) there is a drop in the free-surface downstream of the cylinder that impacts the coherence of the vortex shedding. Irrespective to the relative submergence, the close location of the cylinder to the bottom wall generates an asymmetric von-Kármán vortex street. Proper Orthogonal Decomposition (POD) is used to analyse the spatio-temporal coherence of the turbulent structures shed in the cylinder wake. The spatial patterns of the first two POD modes, those containing the most energy, depict the von-Kármán vortices. As \(Fr\) increases, the energy content of the first pair of POD modes decreases from 56\% at \(Fr=0.26\) to 26.8\% at \(Fr=0.53\), as large-scale vortices lose coherence more rapidly with shallower conditions. This energy redistribution leads to the smaller flow structures to contain a relatively higher energy when \(Fr\) is larger. The frequency of the dominating vortex shedding determined from the spectra of the POD temporal coefficients unveils that the first two coefficients feature a dominant peak at the von-Kármán vortex shedding frequency. At \(Fr < 0.45\), the reconstructed flow field using the first 20 POD modes agrees well with the instantaneous velocities from LES, whereas free-surface effects on the wake dynamics at increasing \(Fr\) requires more POD modes to reconstruct the flow field with reduced error.Data-driven RANS closures for three-dimensional flows around bluff bodieshttps://zbmath.org/1521.761132023-11-13T18:48:18.785376Z"Huijing, Jasper P."https://zbmath.org/authors/?q=ai:huijing.jasper-p"Dwight, Richard P."https://zbmath.org/authors/?q=ai:dwight.richard-p"Schmelzer, Martin"https://zbmath.org/authors/?q=ai:schmelzer.martinSummary: In this short note we apply the recently proposed data-driven RANS closure modelling framework of
the last author et al. [``Discovery of algebraic Reynolds-stress models using sparse symbolic regression'', Flow Turbul. Combust. 104, 579--603 (2020; \url{doi:10.1007/s10494-019-00089-x})]
to fully three-dimensional, high Reynolds number flows: namely wall-mounted cubes and cuboids at \(\operatorname{Re} = 40 , 000\), and a cylinder at \(\operatorname{Re} = 140 , 000\). For each flow, a new RANS closure is generated using sparse symbolic regression based on LES or DES reference data. This new model is implemented in a CFD solver, and subsequently applied to prediction of the other flows. We see consistent improvements compared to the baseline \(k - \omega\) SST model in predictions of mean-velocity in complete flow domain.Large-eddy simulations of the flow over a semi-circular cylinder at Re = 50000https://zbmath.org/1521.761142023-11-13T18:48:18.785376Z"Lysenko, Dmitry A."https://zbmath.org/authors/?q=ai:lysenko.dmitry-a"Donskov, Mark"https://zbmath.org/authors/?q=ai:donskov.mark"Ertesvåg, Ivar S."https://zbmath.org/authors/?q=ai:ertesvag.ivar-sSummary: Large-eddy simulations (LES) of the flow over a semi-circular cylinder at a diameter-based Reynolds number 50000 and zero angle of attack are presented. In comparison with the prominent benchmark flows past circular and square cylinders, this test problem has been less investigated in the literature from both numerical and experimental perspectives. Also, this case can be even more challenging for validation and verification of the computational codes due to a negative lift force, which characterizes this flow regime. A standard numerical platform based on a second-order finite volume method and the \(k\)-equation eddy viscosity subgrid scale model and its dynamic version, implemented in the OpenFOAM CFD toolbox, is used for the present LES. A detailed spectral analysis is provided to examine dynamics of the vortex shedding and shear layer instabilities. The moderate Reynolds number is chosen in order to replicate experimental data, which is limited to integral flow parameters like the lift, drag and pressure coefficients and a Strouhal number. The numerical and experimental data available for the flows over the circular and square cylinders at the Reynolds number \(20000 - 50000\) are used for qualitative assessment of the present results. Similarity of the turbulent wakes between the circular, square and semi-circular cylinders are discussed and compared both, for the integral flow parameters and high order statistics as well. Overall, present simulations provide reasonable agreement with available measurements and numerical calculations. Consistency and satisfactory agreement with the previous numerical and experimental results obtained for the circular and square cylinders are shown as well.Analysis of momentum recovery within the near wake of a cross-flow turbine using large eddy simulationhttps://zbmath.org/1521.761152023-11-13T18:48:18.785376Z"Posa, Antonio"https://zbmath.org/authors/?q=ai:posa.antonioSummary: Momentum recovery within the near wake of a cross-flow turbine is studied, focusing on the different terms of the momentum balance equation. The flow is computed via Large-Eddy Simulation, coupled with an Immersed-Boundary method. Results demonstrate the dominant role of the spanwise flows (oriented along the axis of the turbine) in contributing to momentum recovery within the near wake, especially via advection in the vicinity of its spanwise boundaries and via turbulent transport at inner locations, closer to the mid span. Large streamwise-oriented vortices on the windward side promote momentum recovery into the wake core from its spanwise boundaries, moving the lower-momentum fluid downstream of the turbine from the leeward side towards the windward side, increasing this way the asymmetry of the wake system. Away from the turbine the importance of the spanwise flows declines, compared to that of the cross-stream ones (orthogonal to the axis of the turbine), due to a faster depletion of the spanwise gradients within the wake. As a consequence, the relative importance of the cross-stream flows on further momentum recovery becomes more significant. Meanwhile, as mean gradients decay away from the turbine, turbulent transport contributes more than advection to complete the process of momentum replenishment within the wake.Characteristic spanwise length scales of streamwise vortical structures in the wake of a circular cylinder at \(Re = 1500\) measured via global and local approacheshttps://zbmath.org/1521.761162023-11-13T18:48:18.785376Z"Sarwar, Wasim"https://zbmath.org/authors/?q=ai:sarwar.wasim"Mansy, Reda El"https://zbmath.org/authors/?q=ai:mansy.reda-el"Bergadà, Josep M."https://zbmath.org/authors/?q=ai:bergada.josep-m"Mellibovsky, Fernando"https://zbmath.org/authors/?q=ai:mellibovsky.fernandoSummary: Wake characteristics of the flow past a circular cylinder are analysed in detail at Reynolds number \(Re = 1500\) via direct numerical simulation. A periodic spanwise domain of length \(1 . 5 \pi D\) has been found to yield correct first- and second-order wake statistics in remarkable agreement with published results at the same and closeby \(\mathit{Re} \). A Kelvin-Helmholtz instability with a frequency \(f_{\operatorname{KH}} \simeq 0 . 666\) is observed to occur intermittently in the shear layers issued from the top and bottom of the cylinder. The three-dimensional patterns in the wake have an estimated spanwise length scale \(l_z^1 / D \simeq 0 . 70\) (D is the cylinder diameter) in the near-wake at \(( x , y ) / D = ( 3 , 0 . 5 )\), downstream from the cylinder, when quantified by autocorrelation (global approach). When using the Hilbert-transform (local approach) instead, the predicted length scale of streamwise vortical structures is distributed around \(\lambda_z / D \simeq 0 . 33\) at the same sampling location. Our results show that the two approaches measure different aspects of three-dimensionality: while the former informs of the typical spanwise spacing of streamwise vortices, the latter quantifies the local spanwise size of these same flow structures.An energy-based coupling approach to nonlocal interface problemshttps://zbmath.org/1521.761172023-11-13T18:48:18.785376Z"Capodaglio, Giacomo"https://zbmath.org/authors/?q=ai:capodaglio.giacomo"D'Elia, Marta"https://zbmath.org/authors/?q=ai:delia.marta"Bochev, Pavel"https://zbmath.org/authors/?q=ai:bochev.pavel-b"Gunzburger, Max"https://zbmath.org/authors/?q=ai:gunzburger.max-dSummary: Nonlocal models provide accurate representations of physical phenomena ranging from fracture mechanics to complex subsurface flows, settings in which traditional partial differential equation models fail to capture effects caused by long-range forces at the microscale and mesoscale. However, the application of nonlocal models to problems involving interfaces, such as multimaterial simulations and fluid-structure interaction, is hampered by the lack of a physically consistent interface theory which is needed to support numerical developments and, among other features, reduces to classical models in the limit as the extent of nonlocal interactions vanish. In this paper, we use an energy-based approach to develop a formulation of a nonlocal interface problem which provides a physically consistent extension of the classical perfect interface formulation for partial differential equations. Numerical examples in one and two dimensions validate the proposed framework and demonstrate the scope of our theory.Energetics and mixing of thermally driven flows in Hele-Shaw cellshttps://zbmath.org/1521.761182023-11-13T18:48:18.785376Z"Ulloa, Hugo N."https://zbmath.org/authors/?q=ai:ulloa.hugo-n"Letelier, Juvenal A."https://zbmath.org/authors/?q=ai:letelier.juvenal-aThis paper is concerned with the Rayleigh-Bénard convection in Hele-Shaw cells, which could describe the heat transfer and some mixed fluid flows across the Earth's lithosphere. The authors give new expressions for energy transfer rates, related with the results of \textit{K. B. Winters} et al. [J. Fluid Mech. 289, 115--128 (1995; Zbl 0858.76095)]. Moreover, a new decomposition of the gravitational potential energy is introduced. The Hele-Shaw model given in [the second author et al., J. Fluid Mech. 864, 746--767 (2019; Zbl 1415.76606)], which ``represents a `mathematical bridge' between the Darcy and Navier-Stokes models'' is used -- see System (2.2). A careful analytical analysis of this model is given in Sections 2 and 3. The evolution equation for the temperature is analysed in details. Related with the 3-D model for Rayleigh-Bénard convection described in [\textit{G. O. Hughes} et al., J. Fluid Mech. 729, Paper No. R3, 9 p. (2013; Zbl 1291.76294)], the authors obtain analytical expressions for the energetics in terms of the Rayleigh number and the global Nusselt number. Numerical results for System (2.2) are given in Section 5, by using the solver ``Flow-solve'' described in [\textit{K. B. Winters} and \textit{A. De La Fuente}, Ocean Model. 49--50, 47--59 (2012; \url{doi:10.1016/j.ocemod.2012.04.001})]. The obtained results are very important for understanding ``the heat transfer processes across fractures in the Earth's lithosphere, as well as fractured environments found in the frozen surface of the moons Enceladus and Europa'' -- see the end of Section 7. The last part of the paper contains five appendices. Some very interesting details on obtaining the flow model of System (2.2) are given in Appendix C, by using the Navier-Stokes equation and the advection-diffusion equation for heat transfer, in the frame of Boussinesq approximation. The non-dimensional background potential energy of the 3-D Hele-Shaw geometry is analysed in Appendix E.
Reviewer: Gelu Paşa (Bucureşti)Thermocapillary motion of two viscous liquids in a cylindrical pipehttps://zbmath.org/1521.761192023-11-13T18:48:18.785376Z"Andreev, Viktor K."https://zbmath.org/authors/?q=ai:andreev.viktor-konstantinovich"Kuznetsov, Vladimir V."https://zbmath.org/authors/?q=ai:kuznetsov.vladimir-vSummary: A study is made of an invariant solution of the equations motion of a viscous heat-conducting fluids, which is treated as unidirectional motion in a circular pipe with a common interface under the action of the thermocapillary force. A priori estimates of the velocity and temperature are obtained. The steady state is determined and it is shown that, at larger times, this state is the limiting one. It was established that the thermocapillary effect with surface curvature can induce the return flow. Using Laplace transformation properties the exact analytical solution was constructed. Some examples of numerical reconstruction of the velocities fields depending on geometric and physical parameters were considered.A simple static contact angle-based mesh-dependency correction for 3D capillary flow simulationshttps://zbmath.org/1521.761202023-11-13T18:48:18.785376Z"Castonguay, Samuel"https://zbmath.org/authors/?q=ai:castonguay.samuel"Gervais, Thomas"https://zbmath.org/authors/?q=ai:gervais.thomasSummary: Precise modeling of contact angle is ubiquitous in capillary driven multiphase flow simulations. From a simple 2D rectangular capillary benchmark, we demonstrate and discuss the dependence of capillary dynamics on the mesh size with respect to Washburn's equation. Mesh-dependency is dominated by an underestimation of viscous losses for coarser meshes and transits to ever increasing stress-related errors due the Navier-Stokes equations breaking down in the vicinity of moving contact lines subjected to several known boundary conditions. Furthermore, computational limits generally impose mesh sizes for which none of the errors are negligible. We show that for Washburn-like flows, a simple modification of the static contact angle value is adequate to correct the dynamics of the flow. This semi-analytic correction has the advantage of requiring no modification of the source code or implementation of new boundary conditions, and thus can be easily used with any codes whether commercial or not. Simulations of a self-coalescence module and a capillary pump are presented as 3D verification test cases of the method.A contact line force model for the simulation of drop impacts on solid surfaces using volume of fluid methodshttps://zbmath.org/1521.761212023-11-13T18:48:18.785376Z"Esteban, Adolfo"https://zbmath.org/authors/?q=ai:esteban.adolfo"Gómez, Pablo"https://zbmath.org/authors/?q=ai:gomez.pablo"Zanzi, Claudio"https://zbmath.org/authors/?q=ai:zanzi.claudio"López, Joaquín"https://zbmath.org/authors/?q=ai:lopez.joaquin"Bussmann, Markus"https://zbmath.org/authors/?q=ai:bussmann.markus"Hernández, Julio"https://zbmath.org/authors/?q=ai:hernandez.julio-j|hernandez.julio-cesar|hernandez.julio-lopez|hernandez.julio-aSummary: Characterizing the contact line dynamics on solid walls is often a crucial problem encountered in the simulation of complex interfacial unsteady flows, such as drop impacts on solid surfaces. In this work, a new model is proposed to reproduce the contact line dynamics in a simple but effective way, based on introducing in the momentum equation a force term proportional to the deviation of the calculated contact angle from the value predicted by a dynamic model that takes into account wettability hysteresis. The model has been implemented in a volume of fluid (VOF) method and is applied to the simulation of drop impacts leading to deposition outcomes, although it could be extended to other interface tracking methods and is also applicable to more complex drop impacts involving fingering and splashing. Numerous tests have been performed to evaluate the accuracy and robustness of the proposed model over a wide range of Reynolds and Weber numbers. The results substantially improve those obtained by imposing only the contact angle as a boundary condition at the contact line, and satisfactorily predict a variety of experimental results from the literature for very different impact and wettability conditions.Stationary flow of three fluids in a flat layer under the influence of thermocapillary forces and pressure differencehttps://zbmath.org/1521.761222023-11-13T18:48:18.785376Z"Lemeshkova, Elena N."https://zbmath.org/authors/?q=ai:lemeshkova.elena-nikolaevnaSummary: The unidirectional movement of the three viscous liquids under the influence of thermocapillary forces and pressure difference in a layer restricted by solid walls was researched. The exact stationary decision of the problem has been found.Assessment of RANS-based turbulence model for forced plume dynamics in a linearly stratified environmenthttps://zbmath.org/1521.761232023-11-13T18:48:18.785376Z"Kumar, Nitin"https://zbmath.org/authors/?q=ai:kumar.nitin"Mukherjee, Partho"https://zbmath.org/authors/?q=ai:mukherjee.partho"Chalamalla, Vamsi Krishna"https://zbmath.org/authors/?q=ai:chalamalla.vamsi-krishna"Dewan, Anupam"https://zbmath.org/authors/?q=ai:dewan.anupam"Balasubramanian, Sridhar"https://zbmath.org/authors/?q=ai:balasubramanian.sridharSummary: We present a computational study on the dynamics of a forced plume released in a linearly stratified medium for a range of buoyancy frequencies \(N_\infty =0 - 0.7 s^{-1}\). Three dimensional unsteady Reynolds-Averaged Navier-Stokes (RANS) simulations are performed using the standard \(k - \varepsilon\) turbulence model. The mean flow parameters such as the maximum height \(Z_m\), mean centerline velocity \(\langle w_c \rangle \), mean axial velocity \(\langle w \rangle \), and turbulence parameters such as shear production \((P)\), buoyancy production \((B)\), and dissipation rate \(( \varepsilon )\) are compared with the experimental results of \textit{H. N. Mirajkar} et al. [``Piv study of the dynamics of a forced plume in a stratified ambient'', J. Flow Vis. Image Process 27, No. 1, 29--45 (2020; \url{doi:10.1615/JFlowVisImageProc.2020031059})] and a good agreement is found. The validated model is then used to study the forced plume characteristics and energetics at various values of \(N_\infty \). The passive scalar contours reveal that the plume reaches a maximum height in a stratified medium where the momentum becomes zero, then falls back to the neutral buoyancy height before spreading in the lateral direction. We also found that the maximum height reached by the plume decreases with increasing value of \(N_\infty \), consistent with the previous studies. Quantification of turbulence parameters reveal that the production flux, \(P\), and viscous dissipation, \( \varepsilon \), from the RANS computation are in reasonable agreement with the experimental values at \(N_\infty = 0.4 s^{-1}\). Further, the residual, given by \(\langle \langle P \rangle \rangle + \langle \langle B \rangle \rangle - \langle \langle \varepsilon \rangle \rangle \), is found to be larger for higher \(N_\infty \), indicating more non-homogeneity in the flow at higher stratification. Overall, the RANS modeling is found to accurately predict the mean flow quantities, such as mean centerline velocity and maximum height reached by the plume. The comparison of the modeled turbulence quantities with experimental data seems satisfactory, but indicates a need for some improvement at high values of \(N_\infty \).Robust preconditioned one-shot methods and direct-adjoint-looping for optimizing Reynolds-averaged turbulent flowshttps://zbmath.org/1521.761242023-11-13T18:48:18.785376Z"Nabi, S."https://zbmath.org/authors/?q=ai:nabi.saleh"Grover, P."https://zbmath.org/authors/?q=ai:grover.piyush"Caulfield, C. P."https://zbmath.org/authors/?q=ai:caulfield.c-pSummary: We compare the performance of direct-adjoint-looping (DAL) and one-shot methods in a design optimization task involving turbulent flow modeled using Reynolds-Averaged-Navier-Stokes equations. Two preconditioned variants of the one-shot algorithm are proposed and tested. The role of an approximate Hessian as a preconditioner for the one-shot method iterations is highlighted. We find that the preconditioned one-shot methods can solve the PDE-constrained optimization problem with the cost of computation comparable (about fourfold) to that of the simulation run alone. This cost is substantially less than that of DAL, which requires \(\mathcal{O}(10)\) direct-adjoint loops to converge. The optimization results arising from the one-shot method can be used for optimal sensor/actuator placement tasks, or to provide a reference trajectory to be used for online feedback control applications.Greedy non-intrusive reduced-order model's application in dynamic blowing and suction flow control to suppress the flow separationhttps://zbmath.org/1521.761252023-11-13T18:48:18.785376Z"Wang, Chen"https://zbmath.org/authors/?q=ai:wang.chen.2|wang.chen"Qi, Zheng"https://zbmath.org/authors/?q=ai:qi.zheng"Zheng, Yu"https://zbmath.org/authors/?q=ai:zheng.yu.3"Duan, Huishen"https://zbmath.org/authors/?q=ai:duan.huishen"Chen, Anhong"https://zbmath.org/authors/?q=ai:chen.anhong"Du, Fan"https://zbmath.org/authors/?q=ai:du.fan"Xu, Jiakuan"https://zbmath.org/authors/?q=ai:xu.jiakuan"Li, Guoshu"https://zbmath.org/authors/?q=ai:li.guoshu"Xia, Qiang"https://zbmath.org/authors/?q=ai:xia.qiangSummary: The Greedy Non-Intrusive Reduced-Order Model (GNIROM) is applied in dynamic blowing and suction's flow control to suppress the GAW1 airfoil's flow separation. The effects of the uniform blowing and uniform suction on the flow fields and aerodynamic coefficients have been studied firstly. By comparing a uniform suction control with a dynamic blowing and suction control, it has been found that the dynamic blowing and suction can provide a higher lift coefficient and a lower energy loss. Finally, for the sake of achieving an optimal dynamic blowing and suction control, an optimization of the dynamic blowing and suction's parameters is taken based on the GNIROM, consisting of a Non-Intrusive ROM (NIROM) built by the two-level POD and Radial Basis Function (RBF), and the relative greedy method. A cost function has been proposed by considering suppressing the flow separation, improving the lift-drag characteristics and reducing the energy loss together. The GNIROM has been built for unsteady vorticity fields with the parameters of the dynamic blowing and suction varying. Based on the GNIROM's approximation, the optimal control parameters' values have been determined quickly. Compared to the initial dynamic blowing and suction control, the optimal one has reduced the drag coefficient by 43.4 percents and the energy loss by 42 percents.Shape optimization for an obstacle located in incompressible Boussinesq flowhttps://zbmath.org/1521.761262023-11-13T18:48:18.785376Z"Yan, Wenjing"https://zbmath.org/authors/?q=ai:yan.wenjing"Li, Yingyuan"https://zbmath.org/authors/?q=ai:li.yingyuan"Hou, Jiangyong"https://zbmath.org/authors/?q=ai:hou.jiangyongSummary: In this paper, the shape optimal control for an obstacle immersed in the incompressible fluid governed by Boussinesq equations is investigated. The purpose of this work is to find the optimal shape that minimizes two types of cost functionals. The continuous adjoint method is applied to formulate and implement the nonlinear and strongly coupled system, which can avoid the differentiation of the state system. Then, the Eulerian derivative of the cost functional is derived by involving a Lagrangian functional based on the function space parametrization technique. Finally, the numerical examples of the shape inverse problem and the minimization of energy dissipation are presented to verify the feasibility and effectiveness of the proposed method.Linear instabilities of pulsatile plane channel flow between compliant wallshttps://zbmath.org/1521.761282023-11-13T18:48:18.785376Z"Lebbal, Smail"https://zbmath.org/authors/?q=ai:lebbal.smail"Alizard, Frédéric"https://zbmath.org/authors/?q=ai:alizard.frederic"Pier, Benoît"https://zbmath.org/authors/?q=ai:pier.benoitSummary: The linear dynamics of perturbations developing in an infinite channel with compliant walls is investigated for pulsatile flow conditions. Two-dimensional modal perturbations are considered for Womersley-type pulsating base flows and the wall motion is only allowed in the normal direction. It is found that the flow dynamics is mainly governed by four control parameters: the Reynolds number \(Re\), the reduced velocity \(V_R\), the Womersley number \(Wo\) and the amplitude of the base-flow modulation \(\tilde{Q}\). Linear stability analyses are carried out within the framework of Floquet theory, implementing an efficient approach for removing spurious eigenmodes. The characteristics of flow-based (Tollmien-Schlichting) and wall-based (both travelling-wave flutter and divergence) modes are investigated over a large control-parameter space. It is shown that travelling-wave flutter (TWF) modes are predominantly influenced by the reduced velocity and that the Reynolds number has only a marginal effect. The critical reduced velocity (corresponding to onset of linear instability) is demonstrated to depend both on the Womersley number and modulation amplitude for a given set of wall parameters. Similarly to the steady flow case, the Tollmien-Schlichting (TS) mode is also found to be only weakly affected by the flexibility of the wall in pulsatile flow conditions. Finally, the classification given by \textit{T. B. Benjamin} [J. Fluid Mech. 16, 436--450 (1963; Zbl 0116.19103)] is found to be too restrictive in the case of pulsatile base flows. In particular, a new type of mode is identified that shares characteristics of two distinct Floquet eigenmodes: TS and TWF modes. Due to coupling of the different Floquet harmonics, a phenomenon specific to time-periodic base flows, this two-wave mode exhibits a beating over the intracyclic dynamics.Stability and dynamics of the flow past a bullet-shaped blunt body moving in a pipehttps://zbmath.org/1521.761322023-11-13T18:48:18.785376Z"Bonnefis, Paul"https://zbmath.org/authors/?q=ai:bonnefis.paul"Fabre, David"https://zbmath.org/authors/?q=ai:fabre.david"Airiau, Christophe"https://zbmath.org/authors/?q=ai:airiau.christopheSummary: The flow past a bullet-shaped blunt body moving in a pipe is investigated through global linear stability analysis (LSA) and direct numerical simulation. A cartography of the bifurcation curves is provided thanks to LSA, covering the range of parameters corresponding to Reynolds number \(Re = [50\text{--}110]\), confinement ratio \(a/A = [ 0.01\text{--}0.92]\) and length-to-diameter ratio \(L/d = [2\text{--}10]\). Results show that the first bifurcation is always a steady bifurcation associated to a non-oscillating eigenmode with azimuthal wavenumber \(m = \pm1\) leading to a steady state with planar symmetry. For weakly confined cases (\(a/A<0.6\)), the second bifurcation is associated to an oscillating mode with azimuthal wavenumber \(m=\pm 1\), as in the unconfined case. On the other hand, for the strongly confined case (\(a/A>0.8\)), a destabilization of non-oscillating modes with \(|m| = 2,3\) and a restabilization of the \(m = \pm1\) eigenmodes are observed. The aspect ratio \(L/d\) is shown to have a minor influence for weakly confined cases and almost no influence for strongly confined cases. Direct numerical simulation is subsequently used to characterize the nonlinear dynamics. The results confirm the steady bifurcation predicted by LSA with excellent agreement for the threshold Reynolds. For weakly confined cases, the second bifurcation is a Hopf bifurcation leading to a periodic, planar-symmetric state in qualitative accordance with LSA predictions. For more confined cases, more complex dynamics is obtained, including a steady state with \(|m| = 3\) geometry and aperiodic states.Structural stability of a porous channel of electrical flow affected by periodic velocitieshttps://zbmath.org/1521.761382023-11-13T18:48:18.785376Z"Alkharashi, Sameh A."https://zbmath.org/authors/?q=ai:alkharashi.sameh-a"Alotaibi, Wafa"https://zbmath.org/authors/?q=ai:alotaibi.wafaSummary: This paper investigates the effect of periodic velocity on the stability of two interfacial waves propagating between three layers of immiscible incompressible fluids. The flow propagates saturated in porous media under the influence of an electric field. The viscous potential theory is used to simplify the mathematical procedure, by which viscosity is accumulated on the separating surface rather than in the bulk of fluids. The dispersion relation is shown to be the result of coupled simultaneous Mathieu equations with complex coefficients. The mathematical difficulty in delaying the two Mathieu equations was overcome using the method of multiple time scales. The stability was discussed analytically and numerically by drawing some diagrams and obtaining the transition curves. In the presence and absence of stream periodicity, the linear stage of interface progress is visualized. Depending on the physical quantities used, it has been determined that the upper fluid speed dampens the wave more than the lower and middle velocities. It was discovered that the viscosity ratio of the upper interface, as opposed to the lower viscosity ratio, helps stabilize the liquid sheet. The upper layer porosity has a dual role depending on the sensitivity and significance of the sheet thickness.Effect of waveform on turbulence transition in pulsatile pipe flowhttps://zbmath.org/1521.761512023-11-13T18:48:18.785376Z"Morón, Daniel"https://zbmath.org/authors/?q=ai:moron.daniel"Feldmann, Daniel"https://zbmath.org/authors/?q=ai:feldmann.daniel"Avila, Marc"https://zbmath.org/authors/?q=ai:avila.marcSummary: Pulsatile flow in a straight pipe is a model system for unsteady internal flows in industrial engineering and physiology. In some parameter regimes, the laminar flow is susceptible to helical perturbations, whose transient energy growth scales exponentially with the Reynolds number (\textit{Re}). In this paper, we link the transient growth of these perturbations to the instantaneous linear instability of the laminar flow. We exploit this link to study the effect of the waveform on turbulence transition by performing linear stability and transient growth analyses of flows driven with different waveforms. We find a higher-energy growth in flows driven with longer low-velocity phases as well as with steeper deceleration and acceleration phases. Finally, we perform direct numerical simulations and show that cases with larger transient growth transition faster to turbulence and exhibit larger turbulence intensities. However, these same cases are also more prone to relaminarisation once turbulence has been established. This highlights that, in pulsatile flows, the linear mechanisms responsible for turbulence transition are distinctly different from the nonlinear mechanisms sustaining turbulence.Stratified inclined duct: direct numerical simulationshttps://zbmath.org/1521.761762023-11-13T18:48:18.785376Z"Zhu, Lu"https://zbmath.org/authors/?q=ai:zhu.lu"Atoufi, Amir"https://zbmath.org/authors/?q=ai:atoufi.amir"Lefauve, Adrien"https://zbmath.org/authors/?q=ai:lefauve.adrien"Taylor, John R."https://zbmath.org/authors/?q=ai:taylor.john-r"Kerswell, Rich R."https://zbmath.org/authors/?q=ai:kerswell.richard-r"Dalziel, Stuart B."https://zbmath.org/authors/?q=ai:dalziel.stuart-b"Lawrence, Gregory A."https://zbmath.org/authors/?q=ai:lawrence.gregory-a"Linden, P. F."https://zbmath.org/authors/?q=ai:linden.paul-fSummary: The stratified inclined duct (SID) experiment consists of a zero-net-volume exchange flow in a long tilted rectangular duct, which allows the study of realistic stratified shear flows with sustained internal forcing. We present the first three-dimensional direct numerical simulations (DNS) of SID to explore the transitions between increasingly turbulent flow regimes first described by
\textit{C. R. Meyer} and \textit{P. F. Linden} [J. Fluid Mech. 753, 242--253 (2014; \url{doi:10.1017/jfm.2014.358 })]. We develop a numerical set-up that faithfully reproduces the experiments and sustains the flow for arbitrarily long times at minimal computational cost. We recover the four qualitative flow regimes found experimentally in the same regions of parameter space: laminar flow, waves, intermittent turbulence and fully developed turbulence. We find good qualitative and quantitative agreement between DNS and experiments and highlight the added value of DNS to complement experimental diagnostics and increase our understanding of the transition to turbulence, both temporally (laminar/turbulent cycles) and parametrically (as the tilt angle of the duct and the Reynolds number are increased). These results demonstrate that numerical studies of SID - and deeper integration between simulations and experiments -- have the potential to lead to a better understanding of stratified turbulence.Turbulence in realistic geometries with moving boundaries: when simulations meet experimentshttps://zbmath.org/1521.761912023-11-13T18:48:18.785376Z"Cappanera, L."https://zbmath.org/authors/?q=ai:cappanera.loic"Debue, P."https://zbmath.org/authors/?q=ai:debue.p"Faller, H."https://zbmath.org/authors/?q=ai:faller.hugues"Kuzzay, D."https://zbmath.org/authors/?q=ai:kuzzay.denis"Saw, E-W."https://zbmath.org/authors/?q=ai:saw.ewe-wei"Nore, C."https://zbmath.org/authors/?q=ai:nore.caroline"Guermond, J.-L."https://zbmath.org/authors/?q=ai:guermond.jean-luc"Daviaud, F."https://zbmath.org/authors/?q=ai:daviaud.francois"Wiertel-Gasquet, C."https://zbmath.org/authors/?q=ai:wiertel-gasquet.c"Dubrulle, B."https://zbmath.org/authors/?q=ai:dubrulle.berengereSummary: Considering the current advances in experimental capabilities in fluid mechanics and the advances in computing power and numerical methods in computational fluid mechanics, a question that naturally arises is whether the two sets of techniques are approaching a level of sophistication sufficiently high to deliver results on turbulent flows in realistic geometries that are comparable. The purpose of this paper is to give elements of answers to this question by considering the so-called von Kármán flow where the fluid in a cylindrical container is driven by two counter-rotating impellers. We compare in the mentioned flow the torque and the flow topology obtained by experiments, direct numerical simulations (DNS), and large eddy simulations (LES) at various Reynolds numbers ranging from \(R_{\mathrm{e}} = \mathcal{O} (10^2)\) to \(R_{\mathrm{e}} = \mathcal{O} (10^5)\). In addition to validating the proposed LES model, the level of agreement that is observed between the numerical and the experimental data shows that the degree of accuracy of each of these techniques is reaching a threshold beyond which it is possible to use each of them with high confidence to explore and better understand turbulence in complex flows at \(R_{\mathrm{e}} = \mathcal{O} (10^5)\) and beyond.Effects of corner chamfers on the extreme pressures on a square cylinder at incidence to a uniform flowhttps://zbmath.org/1521.762022023-11-13T18:48:18.785376Z"Dong, Haotian"https://zbmath.org/authors/?q=ai:dong.haotian"Chen, Liping"https://zbmath.org/authors/?q=ai:chen.liping"Du, Xiaoqing"https://zbmath.org/authors/?q=ai:du.xiaoqing"Fang, Liwen"https://zbmath.org/authors/?q=ai:fang.liwen"Jin, Xiaoyu"https://zbmath.org/authors/?q=ai:jin.xiaoyuSummary: Wind-induced damages to cladding, glass curtain walls, and windows on surfaces of buildings demand further investigation of extreme pressures on a square prism. The flow physics of extreme wind pressures on a square cylinder has not yet been clarified, especially as they relate to corner modifications and flow incidence. Large-eddy simulation is utilized to investigate uniform flow past a standard square cylinder and a chamfered cylinder with a chamfer ratio of 1/7. The Reynolds number is fixed at 22,000, and the incidence angle ranges from \(0^\circ\) to \(45^\circ\). The flow mechanism of extreme pressures is studied through analyses of instantaneous flow structures. The influences of corner modifications on extreme pressures are further investigated. The results show that extreme negative pressures are strong in the non-Gaussian regions, which are observed at the rear corners and sides of the two cylinders and change dramatically as the incidence changes. Two types of flow structures are responsible for the extreme pressures, namely, the intermittent rear-corner vortices caused by reverse-flow separation and the Karman vortices near the rear side. The distribution of extreme pressures is highly three-dimensional, owing to 3D vortex structures at a high Reynolds number. By introducing chamfers, the strength and spanwise variations in the corner vortex are reduced, and extreme pressures are weakened.Quantifying turbulence model uncertainty in Reynolds-averaged Navier-Stokes simulations of a pin-fin array. I: Flow fieldhttps://zbmath.org/1521.762142023-11-13T18:48:18.785376Z"Hao, Zengrong"https://zbmath.org/authors/?q=ai:hao.zengrong"Gorlé, Catherine"https://zbmath.org/authors/?q=ai:gorle.catherineSummary: The assumptions that form the basis for Reynolds stress closure models have been formulated by considering canonical flows. As a result, the accuracy of Reynolds-averaged Navier-Stokes simulations can deteriorate significantly when modeling complex flows, and engineering applications would benefit from methods that can quantify the corresponding uncertainty in the predictions. This paper analyzes the performance of a previously proposed turbulence model uncertainty quantification (UQ) framework for simulations of flow through a pin-fin array. The method is a physics-based, data-free, interval approach that perturbs the Reynolds stress tensor shape towards the three limiting realizable states of anisotropy. The performance of the method is evaluated by determining whether large-eddy simulation results for the quantities of interest are encompassed by the intervals predicted by the UQ method. The results demonstrate that perturbing the stress shapes towards the one-component or two-component limit generally enhances the momentum transport between the bulk flow and wake regions, whereas perturbations towards the three-component limit suppress this transport. For quantities of interest that depend on the mean velocity and pressure field this results in predictions for uncertainty intervals that encompass the reference solution. For the turbulence kinetic energy the method fails to predict an adequate upper bound in regions with larger-scale turbulent structures, and it predicts overly conservative bounds in the pin stagnation regions. Based on these results several suggestions for improving the framework are made.Quantifying turbulence model uncertainty in Reynolds-averaged Navier-Stokes simulations of a pin-fin array. II: Scalar transporthttps://zbmath.org/1521.762152023-11-13T18:48:18.785376Z"Hao, Zengrong"https://zbmath.org/authors/?q=ai:hao.zengrong"Gorlé, Catherine"https://zbmath.org/authors/?q=ai:gorle.catherineSummary: The accuracy of Reynolds-averaged Navier-Stokes results for turbulent scalar transport are affected by epistemic uncertainty in the Reynolds stress model in two ways: by altering the mean velocity field that advects the scalar, and by altering the inputs required for scalar flux models. We investigate these effects by propagating uncertainty in the Reynolds stress model to the prediction of scalar quantities in simulations of a pin-fin heat exchanger. The Reynolds stress model uncertainty is quantified by perturbing the anisotropy of the predicted stress tensor towards the three limiting realizable states. This uncertainty is then propagated to the scalar turbulence transport via the conservation law for the mean scalar and the turbulent scalar flux model. We consider three different scalar flux models that explicitly take the Reynolds stresses as input, and evaluate the performance of the models by verifying if high-fidelity large eddy simulation results are encompassed by the model predictions. The results indicate that the predicted uncertainty depends on both the general level of momentum transport and the most-relevant stress component, which is affected by the anisotropy perturbations. The predictions provide a similar bounding behavior for the overall temperature field as for the momentum field, but fail in bounding the local heat transfer rates in several locations. The bounding behaviors are further analyzed in terms of the predicted uncertainty in the flux magnitude, direction, and divergence to identify opportunities for further improvement of the proposed methods.
For Part I, see [the authors, ibid. 209, Article ID 104642, 8 p. (2020; Zbl 1521.76214)].Direct numerical simulation of different finite cylinders rolling on a horizontal surface: the thickness effects on the aerodynamicshttps://zbmath.org/1521.762192023-11-13T18:48:18.785376Z"Javadi, Ardalan"https://zbmath.org/authors/?q=ai:javadi.ardalanSummary: The flow around a cylinder rolling along a horizontal ground plane is investigated using direct numerical simulation for a Reynolds number based on the cylinder diameter, \(D\), of \(Re_D = 3 \times 10^4\). Three cylinder thicknesses, \(T/D = 0.040\), 0.126, and 0.400, are considered. The time-averaged drag coefficients are found to be 0.87, 0.69, and 0.97 for the three cylinders, respectively. The non-monotonic variation in drag coefficient with thickness suggests a transition in the proportion of contributions of friction and pressure drag to the total drag which changes about 30\% with thickness increase. Indeed, the ratio of friction drag to pressure drag varies from 0.333 to 0.085 and finally to 0.013 for the three cylinders. The pressure coefficient become more negative in the aft of the thicker cylinders, because the cylinder become more bluff body which suggests more pronounced pressure drag. Temporal fluctuations in the drag coefficient associated with vortex shedding events increase monotonically with thickness, though the root-mean-square of the drag coefficient follows the same trend as the mean drag coefficient. The lift coefficients are \(-0.057\), 0.066, and 0.64 for the three respective cylinders. The negative value for the thinnest cylinder indicates down force. The transition from negative lift on the thin cylinder to positive lift on the thick cylinder is associated with elevated surface pressure just upstream of the ground contact point as thickness increases. As the flow is more detached from the cylinder sides, the friction lift is less significant with thickness increase. Furthermore, the pressure coefficient is negative spatially larger in the top of the thicker cylinders which the expansion offers a more significant upward pressure lift.Determining \textit{a priori} a RANS model's applicable range via global epistemic uncertainty quantificationhttps://zbmath.org/1521.762292023-11-13T18:48:18.785376Z"L D. Huang, Xinyi"https://zbmath.org/authors/?q=ai:l-d-huang.xinyi"Jain, Naman"https://zbmath.org/authors/?q=ai:jain.naman"Abkar, Mahdi"https://zbmath.org/authors/?q=ai:abkar.mahdi"F. Kunz, Robert"https://zbmath.org/authors/?q=ai:kunz.robert-f"I. A. Yang, Xiang"https://zbmath.org/authors/?q=ai:i-a-yang.xiangSummary: Calibrating a Reynolds-averaged Navier-Stokes (RANS) model against data leads to an improvement. Determining \textit{a priori} if such an improvement generalizes to flows outside the calibration data is an outstanding challenge. This work attempts to address this challenge via global epistemic Uncertainty Quantification (UQ). Unlike the available epistemic UQ methods that are local and tell us a model's uncertainty at one specific flow condition, the global epistemic UQ method presented in this work tells us also whether a perturbation of the original model would generalize. Specifically, the global epistemic UQ method evaluates a potential improvement in terms of its ``effectiveness'' and ``inconsistency''. Any improvement can be put in one of the following four quadrants: first, high effectiveness, low inconsistency; second, high effectiveness, high inconsistency; third, low effectiveness, low inconsistency; and fourth, low effectiveness, high inconsistency. An improvement would generalize if and only if it is in the high effectiveness, low inconsistency quadrant. To demonstrate the concept, we apply the global epistemic UQ to full Reynolds stress modeling of a stratified shear layer. The global epistemic UQ results point to a model coefficient in the pressure-strain correlation closure (among others) as effective and consistent for predicting the quantity of interest of shear layer's growth. We calibrate the model coefficients such that our RANS matches direct numerical simulation data at one flow condition. We show that the calibrated model generalizes to several other test flow conditions. On the other hand, when calibrating a high inconsistency term, the model does not generalize beyond the calibration condition.Non-explicit large eddy simulations of turbulent channel flows from \(R e_\tau = 180\) up to \(R e_\tau = 5 , 200\)https://zbmath.org/1521.762332023-11-13T18:48:18.785376Z"Mahfoze, Omar A."https://zbmath.org/authors/?q=ai:mahfoze.omar-a"Laizet, Sylvain"https://zbmath.org/authors/?q=ai:laizet.sylvainSummary: This numerical study based on high-order finite-difference schemes presents LES-NWR (Large Eddy Simulation with near-wall resolution) of turbulent channel flows up to \(R e_\tau = 5200\) using non-explicit approaches for which numerical dissipation is introduced via the discretisation of viscous terms of the Navier-Stokes equations. These models are cheaper than explicit LES models as no extra terms are needed in the equations to account for the contribution of the unresolved scales. The Approximate Deconvolution Method with Relaxation Term (ADM-RT) approach is also assessed and the present LES data are compared with reference Direct Numerical Simulations (DNS) data for first and second order moments as well as for the turbulent kinetic energy budget. Even if the viscous sublayer is not resolved, the proposed non-explicit LES approaches are in excellent agreement with the reference DNS data and to a certain extent with the ADM-RT model, for a fraction of the cost of the DNS. The proposed non-explicit models, for which the possibility to locally adjust the added numerical dissipation is investigated, are straightforward to implement and come with a negligible additional computational cost while the ADM-RT model is 30\% more expensive than the non-explicit models. The parameters of the models are defined before the simulations and no modifications of the parameters are needed when the Reynolds number and the mesh resolution are changed. It is shown that a modulation of the magnitude of the numerical dissipation in time and in space is not necessarily needed, at least for the mesh resolutions and Reynolds numbers considered in the present study. The main conclusion is that non-explicit models can replace advantageously explicit models when high-order finite-difference methods are used. They can generate accurate LES-NWR of turbulent channel flows over a wide range of Reynolds numbers at a fraction of a cost of DNS.A turbulent eddy-viscosity surrogate modeling framework for Reynolds-averaged Navier-Stokes simulationshttps://zbmath.org/1521.762362023-11-13T18:48:18.785376Z"Maulik, Romit"https://zbmath.org/authors/?q=ai:maulik.romit"Sharma, Himanshu"https://zbmath.org/authors/?q=ai:sharma.himanshu"Patel, Saumil"https://zbmath.org/authors/?q=ai:patel.saumil-sudhir"Lusch, Bethany"https://zbmath.org/authors/?q=ai:lusch.bethany"Jennings, Elise"https://zbmath.org/authors/?q=ai:jennings.eliseSummary: The Reynolds-averaged Navier-Stokes (RANS) equations for steady-state assessment of incompressible turbulent flows remain the workhorse for practical computational fluid dynamics (CFD) applications. Consequently, improvements in speed or accuracy have the potential to affect a diverse range of applications. We introduce a machine learning framework for the surrogate modeling of steady-state turbulent eddy viscosities for RANS simulations, given the initial conditions. This modeling strategy is assessed for parametric interpolation, while numerically solving for the pressure and velocity equations to steady state, thus representing a framework that is hybridized with machine learning. We achieve competitive steady-state results with a significant reduction in solution time when compared to those obtained by the Spalart-Allmaras one-equation model. This is because the proposed methodology allows for considerably larger relaxation factors for the steady-state velocity and pressure solvers. Our assessments are made for a backward-facing step with considerable mesh anisotropy and separation to represent a practical CFD application. For test experiments with either varying inlet velocity conditions or step heights we see time-to-solution reductions around a factor of 5. The results represent an opportunity for the rapid exploration of parameter spaces that prove prohibitive when utilizing turbulence closure models with multiple coupled partial differential equations.Characterization of the turbulent wake of an axial-flow hydrokinetic turbine via large-eddy simulationhttps://zbmath.org/1521.762462023-11-13T18:48:18.785376Z"Posa, Antonio"https://zbmath.org/authors/?q=ai:posa.antonio"Broglia, Riccardo"https://zbmath.org/authors/?q=ai:broglia.riccardoSummary: Large-Eddy Simulation on a grid composed of about two billion points is utilized to characterize the turbulent wake of an axial-flow hydrokinetic turbine. The dominant role of the tip vortices is revealed, both in the near wake, where they are very coherent, and downstream, after development of instability. As long as the tip vortices are stable, sharp peaks of Reynolds stresses populate the outer boundary of the wake, where turbulence is strongly anisotropic and dominated by the fluctuations of the radial velocity component. Such anisotropy is also confirmed by the shear stresses, with the most significant one tied to the fluctuations of the radial and streamwise velocities, originating from the interaction between tip vortices. When the system of tip vortices develops instability, the behavior of turbulence is substantially modified. The outer maxima become more diffused and move gradually towards the wake core. In contrast with the near wake, the fluctuations of the radial velocity become lower than those of the azimuthal and streamwise velocities. Instead, the shear stress associated to the radial and streamwise velocities keeps the most significant one, contributing to momentum recovery via turbulent transport. The present results demonstrate a strong anisotropy of turbulence within the wake, which should be taken properly into account when lower-fidelity methodologies, relying on turbulence modeling, are utilized to simulate this class of flows.High Reynolds number airfoil turbulence modeling method based on machine learning techniquehttps://zbmath.org/1521.762552023-11-13T18:48:18.785376Z"Sun, Xuxiang"https://zbmath.org/authors/?q=ai:sun.xuxiang"Cao, Wenbo"https://zbmath.org/authors/?q=ai:cao.wenbo"Liu, Yilang"https://zbmath.org/authors/?q=ai:liu.yilang"Zhu, Linyang"https://zbmath.org/authors/?q=ai:zhu.linyang"Zhang, Weiwei"https://zbmath.org/authors/?q=ai:zhang.weiweiSummary: In this paper, a turbulence model based on deep neural network is developed for turbulent flow around airfoil at high Reynolds numbers. According to the data got from the Spalart-Allmaras (SA) turbulence model, we build a neural network model that maps flow features to eddy viscosity. The model is then used to replace the SA turbulence model to mutually couple with the CFD solver. We build this suitable data-driven turbulence model mainly from the inputs, outputs features and loss function of the model. A feature selection method based on feature importance is also implemented. The results show that this feature selection method can effectively remove redundant features. The model based on the new input features has better accuracy and stability in mutual coupling with the CFD solver. The force coefficient obtained from solution can match the sample data well. The developed model also shows strong generalization at different inflow condition (angle of attack, Mach number, Reynolds number and airfoil).Investigation of grid-based vorticity-velocity large eddy simulation off-body solvers for application to overset CFDhttps://zbmath.org/1521.762622023-11-13T18:48:18.785376Z"Whitehouse, Glen R."https://zbmath.org/authors/?q=ai:whitehouse.glen-r"Boschitsch, Alexander H."https://zbmath.org/authors/?q=ai:boschitsch.alexander-hSummary: Accurately predicting unsteady wakes and vortex-dominated flows is essential to a wide range of engineering applications, including aircraft, rotorcraft, shipboard operations, bio-inspired unsteady flight and propulsion, wind turbines, and urban flows. While current CFD software can model the complete flow field and wake system, the computational costs incurred in high Reynolds number unsteady turbulent flow simulations often remain prohibitive for routine engineering use, particularly for applications involving moving components. Prior work has demonstrated that by adopting a vorticity-velocity formulation in a grid-based off-body flow solver (VorTran-M and VorTran-M2) one can lower these costs by several orders of magnitude when compared to conventional approaches. This paper describes the extensions made to VorTran-M2 to support turbulent flows, and associated benchmarking activity to assess its performance for problems involving strong stretching and diffusion processes, whose competing contributions to the vorticity field are core drivers of turbulent flow evolution. Predictions are presented for: (i) the Kida-Pelz problem whose inviscid form is of mathematical interest due to its apparent formation of singular flow in finite time; and (ii) the Taylor Green vortex arrangement, which has been extensively studied as a fundamental simulation challenge in the turbulence modeling community. The results are used to evaluate the overall predictive ability and performance of two sub-grid scale models incorporated into VorTran-M2. Results indicate that the computational cost savings seen previously for inviscid and convection dominated problems extend to turbulent flow simulations supporting the viability of VorTran-M2 as a low cost means for accurately modeling far-field and background flows, particularly when long duration vorticity evolution is of interest.Numerical study on the supersonic near-wake flow structures of a cylinder at an angle of attackhttps://zbmath.org/1521.762922023-11-13T18:48:18.785376Z"Chen, Zhi"https://zbmath.org/authors/?q=ai:chen.zhi"Pan, Honglu"https://zbmath.org/authors/?q=ai:pan.honglu"Zhang, Liang"https://zbmath.org/authors/?q=au:Zhang, LiangSummary: The supersonic near-wake flow experiment conducted by Dutton on a cylinder with 10 degrees angle of attack was studied numerically with Delayed Detached Eddy Simulation (DDES) method. The wind tunnel test section were included in the geometry model to examine if its omission led to the unsuccessful prediction of several important flow features in previous studies. Flow structures were compared to experiment measurements, Gaitonde's \(k- \epsilon\) model results and our previous Monotonically Integrated Large Eddy Simulation (MILES) results. It was revealed that with present geometry model and numerical method, good agreements with wind tunnel experiment result were obtained, including the wave structures, density fields and velocity fields. In particular, the inclusion of wind tunnel test section wall in geometry model reproduces the finite area nozzle exit flow and the expansion wave behind the recirculation zone in the actual experiment setup, which lead to correct prediction of the position of maximum streamwise velocity point. The present simulation also reproduced the uniform pressure profile and value observed in the experiment and the deviation between computation and experiment was within 10\%. The flow field data obtained was further analyzed to investigate the vortex surface shape and recirculation region shape in near wake flow with non-zero angle of attack and significant differences were found compared to the zero angle of attack case. The vortex surfaces show a non-axisymmetric slitting movement in the near wake region, which gives an explanation to the non-circular density contour pattern on streamwise flow field slices. The recirculation region shape was identified with zero isosurface of streamwise velocity and was found to be of complex three-dimensional shape with maximum length beside the symmetry plane and a local minimum at windward side of the symmetry plane, which is significantly different from that of zero angle of attack case. The observation that the length of the recirculation zone was greatly reduced on the symmetry plane at non-zero angle of attack in previous study is due to the aforementioned local minimum on the symmetry plane. The reduction of recirculation length is much less if we consider the three-dimensional shape of the region.A nudged hybrid analysis and modeling approach for realtime wake-vortex transport and decay predictionhttps://zbmath.org/1521.763112023-11-13T18:48:18.785376Z"Ahmed, Shady E."https://zbmath.org/authors/?q=ai:ahmed.shady-e"Pawar, Suraj"https://zbmath.org/authors/?q=ai:pawar.suraj"San, Omer"https://zbmath.org/authors/?q=ai:san.omer"Rasheed, Adil"https://zbmath.org/authors/?q=ai:rasheed.adil"Tabib, Mandar"https://zbmath.org/authors/?q=ai:tabib.mandarSummary: We put forth a long short-term memory (LSTM) nudging framework for the enhancement of reduced order models (ROMs) of fluid flows utilizing noisy measurements for air traffic improvements. Toward emerging applications of digital twins in aviation, the proposed approach allows for constructing a realtime predictive tool for wake-vortex transport and decay systems. We build on the fact that in realistic application, there are uncertainties in initial and boundary conditions, model parameters, as well as measurements. Moreover, conventional nonlinear ROMs based on Galerkin projection (GROMs) suffer from imperfection and solution instabilities, especially for advection-dominated flows with slow decay in the Kolmogorov \(n\)-width. In the presented LSTM nudging (LSTM-N) approach, we fuse forecasts from a combination of imperfect GROM and uncertain state estimates, with sparse Eulerian sensor measurements to provide more reliable predictions in a dynamical data assimilation framework. We illustrate our concept by solving the two-dimensional vorticity transport equation. We investigate the effects of measurements noise and state estimate uncertainty on the performance of the LSTM-N behavior. We also demonstrate that it can sufficiently handle different levels of temporal and spatial measurement sparsity, and offer a huge potential in developing next-generation digital twin technologies for aerospace applications.Development of a high-order continuous Galerkin sharp-interface immersed boundary method and its application to incompressible flow problemshttps://zbmath.org/1521.763162023-11-13T18:48:18.785376Z"Barbeau, Lucka"https://zbmath.org/authors/?q=ai:barbeau.lucka"Étienne, Stéphane"https://zbmath.org/authors/?q=ai:etienne.stephane"Béguin, Cédric"https://zbmath.org/authors/?q=ai:beguin.cedric"Blais, Bruno"https://zbmath.org/authors/?q=ai:blais.brunoSummary: The sharp-interface immersed boundary method is a strategy to impose boundary conditions on complex geometries while simplifying the meshing process. This method can offer a high-order of accuracy. Most sharp-interface methods have been developed in the context of the finite volume or the finite difference methods. In this paper, we introduce, verify and validate a novel high-order sharp-interface immersed boundary method in the context of the finite element method. We apply this method to the incompressible Navier-Stokes equations using a pressure-stabilizing/Petrov-Galerkin (PSPG) stabilization. We verify that we obtain a high order of convergence using a Taylor-Couette flow. We validate the results obtained for the drag, lift, and Strouhal number of the flow behind a cylinder at \(R e = 200\). We investigate the flow around a sphere at \(R e = 100\) and compare the drag force and the characteristics of the recirculating zones with experimental and numerical results obtained in the literature. Finally, the sharp-interface method is used to study a packing of 10 spheres at \(R e = 50\), and the results are compared to those obtained with a conformal mesh. It is shown that the sharp-interface immersed boundary preserves the high-order of the finite element scheme and accurately predicts the steady-state and transient flow around particles including the evaluation of the particle-fluid forces.Data-driven robust state estimation for reduced-order models of 2D Boussinesq equations with parametric uncertaintieshttps://zbmath.org/1521.763182023-11-13T18:48:18.785376Z"Benosman, Mouhacine"https://zbmath.org/authors/?q=ai:benosman.mouhacine"Borggaard, Jeff"https://zbmath.org/authors/?q=ai:borggaard.jeff-tSummary: A robust, low-order POD-based state estimator, also known as an observer, for the challenging fluid-dynamics test-case of uncertain 2D Boussinesq equations is presented in this paper. The observer design is based on the methodology recently introduced by the \(authors^1\), which incorporates robustness to bounded model uncertainties, and data-driven auto-tuning of the observer gains. An extensive numerical study on \textit{the 2D Boussinesq equations with parametric uncertainties} demonstrates the performance of our observer. The reported numerical results show that the proposed observer allows estimation of the complete temperature and velocity fields from a reduced number of measurements. It is also shown that the proposed observer is robust to changes or errors in the value of the Reynolds number. In other words, we show that we can design the observer based on an assumed uncertain value for the Reynolds number, and be able to estimate the temperature and velocity solutions corresponding to actual Reynolds number.Stabilized reduced-order models for unsteady incompressible flows in three-dimensional parametrized domainshttps://zbmath.org/1521.763202023-11-13T18:48:18.785376Z"Buoso, Stefano"https://zbmath.org/authors/?q=ai:buoso.stefano"Manzoni, Andrea"https://zbmath.org/authors/?q=ai:manzoni.andrea"Alkadhi, Hatem"https://zbmath.org/authors/?q=ai:alkadhi.hatem"Kurtcuoglu, Vartan"https://zbmath.org/authors/?q=ai:kurtcuoglu.vartanSummary: In this work we derive a parametric reduced-order model (ROM) for the unsteady three-dimensional incompressible Navier-Stokes equations without additional pre-processing on the reduced-order subspaces. Concerning the high-fidelity, full-order model, we start from a streamline-upwind Petrov-Galerkin stabilized finite element discretization of the equations using \(\mathbb{P}^1 -\mathbb{P}^1\) elements for velocity and pressure, respectively. We rely on Galerkin projection of the discretized equations onto reduced basis subspaces for the velocity and the pressure, respectively, obtained through Proper Orthogonal Decomposition on a dataset of snapshots of the full-order model. Both nonlinear and nonaffinely parametrized algebraic operators of the reduced-order system of nonlinear equations, including the projection of the stabilization terms, are efficiently assembled exploiting the Discrete Empirical Interpolation Method (DEIM), and its matrix version (MDEIM), thus obtaining an efficient \textit{offline}-\textit{online} computational splitting. We apply the proposed method to \textit{(i)} a two-dimensional lid-driven cavity flow problem, considering the Reynolds number as parameter, and \textit{(ii)} a three-dimensional pulsatile flow in stenotic vessels characterized by geometric and physiological parameter variations. We numerically show that the projection of the stabilization terms on the reduced basis subspace and their reconstruction using (M)DEIM allows to obtain a stable ROM with coupled velocity and pressure solutions, without any need for enriching the reduced velocity space, or further stabilizing the ROM. Additionally, we demonstrate that our implementation allows to compute the ROM solution about 20 times faster than the full order model.A POD-Galerkin reduced order model for the Navier-Stokes equations in stream function-vorticity formulationhttps://zbmath.org/1521.763332023-11-13T18:48:18.785376Z"Girfoglio, Michele"https://zbmath.org/authors/?q=ai:girfoglio.michele"Quaini, Annalisa"https://zbmath.org/authors/?q=ai:quaini.annalisa"Rozza, Gianluigi"https://zbmath.org/authors/?q=ai:rozza.gianluigiSummary: We develop a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for the efficient numerical simulation of the parametric Navier-Stokes equations in the stream function-vorticity formulation. Unlike previous works, we choose different reduced coefficients for the vorticity and stream function fields. In addition, for parametric studies we use a global POD basis space obtained from a database of time dependent full order snapshots related to sample points in the parameter space. We test the performance of our ROM strategy with the well-known vortex merger benchmark and a more complex case study featuring the geometry of the North Atlantic Ocean. Accuracy and efficiency are assessed for both time reconstruction and physical parameterization.A segregated spectral element method for the 2D transient incompressible Navier-Stokes equationshttps://zbmath.org/1521.763372023-11-13T18:48:18.785376Z"He, Wenqiang"https://zbmath.org/authors/?q=ai:he.wenqiang"Qin, Guoliang"https://zbmath.org/authors/?q=ai:qin.guoliang"Wang, Yazhou"https://zbmath.org/authors/?q=ai:wang.yazhou"Bao, Zhenzhong"https://zbmath.org/authors/?q=ai:bao.zhenzhongSummary: In this paper, a spectral element method for the solution of the two-dimensional transient incompressible Navier-Stokes equations is introduced, which combines the segregated velocity-pressure equal-order formulation originated from the SIMPLE (semi-implicit method for pressure linked equations) algorithm. In contrast to previous segregated finite element method based on the SIMPLE algorithm, the pressure equation is derived from the momentum and continuity equations using the element matrices to ensure the convergence of the pressure. High-order element basis functions are adopted to construct the discrete form that presents arbitrary order or accuracy. The validation test with analytical solution verifies the high accuracy of the method. The flow in a lid-driven cavity with different inclination angles and the flow over a backward-facing step are investigated to further illustrate the property of the scheme. The computed results are in excellent agreement with the benchmark solutions, even if fewer grid points are used. The almost periodic solution for the flow of \(Re=10000\) in a lid-driven square cavity is also captured by the present scheme. The numerical results indicate that the proposed high-order method can significantly reduce the number of grid points used in the calculation.An implementation of MPI and hybrid OpenMP/MPI parallelization strategies for an implicit 3D DDG solverhttps://zbmath.org/1521.763382023-11-13T18:48:18.785376Z"He, Xiaofeng"https://zbmath.org/authors/?q=ai:he.xiaofeng"Wang, Kun"https://zbmath.org/authors/?q=ai:wang.kun.2"Feng, Yiwei"https://zbmath.org/authors/?q=ai:feng.yiwei"Lv, Lili"https://zbmath.org/authors/?q=ai:lv.lili"Liu, Tiegang"https://zbmath.org/authors/?q=ai:liu.tiegangSummary: This work describes an implementation of OpenMP, MPI, hybrid OpenMP/MPI parallelization strategies for an implicit three-dimensional (3D) direct discontinuous Galerkin (DDG) solver used for Navier-Stokes equations. Significantly, an efficient local matrix-based MPI parallelization strategy of an implicit DG solver is proposed. Furthermore, we give an implementation of OpenMP and hybrid OpenMP/MPI strategy for comparison. The storage structure based on the local matrix makes the MPI parallelization can easily use the local number to access and assign, the storage is compact and compatible with Block Sparse Row (BSR) format, and the program is easier to modularize. Several numerical tests for 3D Navier-Stokes equations are implemented to indicate the performance of parallelization strategies. For the problem of more than 200 million degrees of freedom, the designed pure MPI strategy for 3rd-order DDG solvers with 2nd-order polynomials (DDG(P2)) can get parallel efficiency of almost 90\% at near ten thousand cores on the Tianhe-2 supercomputer. In particular, the pure MPI parallelization based on local matrix reaches a higher level of parallel efficiency than hybrid OpenMP/MPI parallelization.A novel stabilized Galerkin meshless method for steady incompressible Navier-Stokes equationshttps://zbmath.org/1521.763392023-11-13T18:48:18.785376Z"Hu, Guanghui"https://zbmath.org/authors/?q=ai:hu.guanghui"Li, Ruo"https://zbmath.org/authors/?q=ai:li.ruo"Zhang, Xiaohua"https://zbmath.org/authors/?q=ai:zhang.xiaohuaSummary: In the paper, a novel stabilized meshless method is presented for solving steady incompressible fluid flow problems. For this method, the standard Galerkin discretization is used to momentum equations, where the variational multiscale method is applied to mass conservation equation. Thus, the novel stabilized method can be regarded as a simplification of the variational multiscale element free Galerkin method, but it still retains the advantages of the variational multiscale element free Galerkin method. The present method allows equal linear basis approximation of both velocity and pressure and avoids the Ladyzhenskaya-Babuška-Breezi (LBB) condition. Meanwhile, it can automatically obtain the stabilization tensor. Three Stokes flow and two Navier-Stokes flow problems are applied to validate the accuracy and feasibility of the present method. It is shown that the present stabilized meshless method can guarantee the numerical stability and accuracy for incompressible fluid flow problems. Moreover, it can save computational cost evidently compared with variational multiscale element free Galerkin method.A fast matrix-free approach to the high-order control volume finite element method with application to low-Mach flowhttps://zbmath.org/1521.763432023-11-13T18:48:18.785376Z"Knaus, Robert"https://zbmath.org/authors/?q=ai:knaus.robertSummary: A fast matrix-free formulation of the control volume finite element method is presented, requiring much less memory and computational work than previous efforts. The method is implemented and evaluated as a solver for low-Mach flow, including the evaluation of a preconditioning strategy for the pressure Poisson equation. The efficiency and scaling with polynomial order is evaluated on simple turbulent flows of interest, with appropriate solution quality metrics, and compared with a reference node-centered finite volume discretization. For a turbulent channel flow test, we show improvement in computational work for a given accuracy with the high-order scheme. The performance on a GPU accelerated platform is also investigated, with benefit shown for the matrix-free discretization.A cell-based smoothed finite element method (CS-FEM) for three-dimensional incompressible laminar flows using mixed wedge-hexahedral elementhttps://zbmath.org/1521.763472023-11-13T18:48:18.785376Z"Liu, Mingyang"https://zbmath.org/authors/?q=ai:liu.mingyang"Gao, Guangjun"https://zbmath.org/authors/?q=ai:gao.guangjun"Zhu, Huifen"https://zbmath.org/authors/?q=ai:zhu.huifen"Jiang, Chen"https://zbmath.org/authors/?q=ai:jiang.chen.1"Liu, Guirong"https://zbmath.org/authors/?q=ai:liu.gui-rongSummary: Smoothed finite element method (S-FEM) has attracted lots of attentions in the fields of computational mechanics, especially in solid mechanics and heat transfer problems. In computational fluid dynamics, works on S-FEM were limited to two-dimensional problems. This work aims to extend the S-FEM to three-dimensional (3D) incompressible laminar flows. Wedge element grids and grids with mixed wedge and hexahedral elements are formulated for 3D incompressible laminar flows based on the cell-based S-FEM (CS-FEM). To reduce numerical oscillations, we implemented the streamline-upwind/Petrov-Galerkin method (SUPG) together with the stabilized pressure gradient projection (SPGP). Several examples are presented, including the Beltrami flow, lid-driven cavity flow, backward facing step flow and microchannel flow, to validate and examine the presented method. The results indicate that wedge elements and mixed wedge-hexahedral elements based on the CS-FEM have higher computational efficiency than that of hexahedral elements based on the CS-FEM for the same level of computational accuracy. It is also found that the present CS-FEM performed better than the standard FEM in dealing with pressure stability. The flow characteristics are well captured by the CS-FEM using the mixed wedge-hexahedral elements, and the numerical results are acceptable compared to those of STAR-CCM+.On the development, verification, and validation of a discontinuous Galerkin solver for the Navier-Stokes equationshttps://zbmath.org/1521.763512023-11-13T18:48:18.785376Z"Lohry, Mark W."https://zbmath.org/authors/?q=ai:lohry.mark-w"Martinelli, Luigi"https://zbmath.org/authors/?q=ai:martinelli.luigiSummary: We present \textit{maDG}, a newly developed code designed for the efficient parallel implicit solution of the 3D unstructured nodal discontinuous Galerkin discretization of the unsteady compressible Navier-Stokes equations. The code is being developed to provide an efficient, modular, and maintainable software platform for studying algorithmic and modeling issues arising in high-resolution CFD. In this paper we address some issues pertinent to the software architecture and testing implementation used towards the goal of implicit time integration of discontinuous Galerkin (DG) approximations.A discontinuous Galerkin approximation for a wall-bounded consistent three-component Cahn-Hilliard flow modelhttps://zbmath.org/1521.763532023-11-13T18:48:18.785376Z"Manzanero, Juan"https://zbmath.org/authors/?q=ai:manzanero.juan"Redondo, Carlos"https://zbmath.org/authors/?q=ai:redondo.carlos"Rubio, Gonzalo"https://zbmath.org/authors/?q=ai:rubio.gonzalo"Ferrer, Esteban"https://zbmath.org/authors/?q=ai:ferrer.esteban"Rivero-Jiménez, Ángel"https://zbmath.org/authors/?q=ai:rivero-jimenez.angelSummary: We present a high-order discontinuous Galerkin (DG) discretization for the three-phase Cahn-Hilliard model of
[\textit{F. Boyer} and \textit{C. Lapuerta}, ESAIM, Math. Model. Numer. Anal. 40, No. 4, 653--687 (2006; Zbl 1173.35527)].
Study of a three component Cahn-Hilliard flow model]. In this model, consistency is ensured with an additional term in the chemical free-energy. The model considered in this work includes a wall boundary condition that allows for an arbitrary equilibrium contact angle in three-phase flows. The model is discretized with a high-order discontinuous Galerkin spectral element method that uses the symmetric interior penalty to compute the interface fluxes, and allows for unstructured meshes with curvilinear hexahedral elements. The integration in time uses a first order IMplicit-EXplicit (IMEX) method, such that the associated linear systems are decoupled for the two Cahn-Hilliard equations. Additionally, the Jacobian matrix is constant, and identical for both equations. This allows us to solve the two systems by performing only one LU factorization, with the size of the two-phase system, followed by two Gauss substitutions. Finally, we test numerically the accuracy of the scheme providing convergence analyses for two and three-dimensional cases, including the captive bubble test, the study of two bubbles in contact with a wall and the spinodal decomposition in a cube and in a curved pipe with a ``T'' junction.An adaptive enriched semi-Lagrangian finite element method for coupled flow-transport problemshttps://zbmath.org/1521.763582023-11-13T18:48:18.785376Z"Ouardghi, Abdelouahed"https://zbmath.org/authors/?q=ai:ouardghi.abdelouahed"El-Amrani, Mofdi"https://zbmath.org/authors/?q=ai:el-amrani.mofdi"Seaid, Mohammed"https://zbmath.org/authors/?q=ai:seaid.mohammedSummary: An adaptive enriched semi-Lagrangian finite element method is proposed for the numerical solution of coupled flow-transport problems on unstructured triangular meshes. The new method combines the semi-Lagrangian scheme to deal with the convection terms, the finite element discretization to manage irregular geometries, a direct conjugate-gradient algorithm to solve the generalized Stokes problem, and an adaptive \(\mathrm{L}^2\)-projection using quadrature rules to improve the efficiency and accuracy of the proposed method. In this study, the gradient of the temperature is used as an error indicator for the adaptation of enrichments by increasing the number of quadrature points where it is needed without refining the computational mesh. Unlike other adaptive finite element methods for coupled flow-transport problems, linear systems in the proposed enriched semi-Lagrangian finite element method preserve the same structure and size at each refinement in the adaptation procedure. In addition, due to the Lagrangian treatment of convection terms in this approach, the standard Courant-Friedrichs-Lewy condition is relaxed and the time truncation errors are reduced in the diffusion-reaction part. We assess the performance of the proposed method for a convection-diffusion problem with a known analytical solution and for the benchmark problem of thermal flow past a circular cylinder. We also solve a heat transport problem in the Mediterranean Sea to illustrate the ability of the method to resolve complex flow features in irregular geometries. Comparisons to the conventional semi-Lagrangian finite element method are also carried out in the current work. The obtained numerical results demonstrate the potential of the proposed method to capture the main flow features and support our expectations for an accurate and highly efficient enriched semi-Lagrangian finite element method for coupled flow-transport problems.A dual mesh finite domain method for steady-state convection-diffusion problemshttps://zbmath.org/1521.763612023-11-13T18:48:18.785376Z"Reddy, J. N."https://zbmath.org/authors/?q=ai:reddy.junuthula-narasimha"Martinez, Matthew"https://zbmath.org/authors/?q=ai:martinez.matthewSummary: The \textit{dual-mesh finite domain method} (DMFDM) proposed by the first author [``A dual mesh finite domain method for the numerical solution of differential equations'', Int. J. Comput. Methods Eng. Sci. Mech. 20, No. 3, 212--228 (2019; \url{doi:10.1080/15502287.2019.16109})] is used to study the steady-state convection-diffusion problems in 1D and 2D. In the DMFDM, one mesh of finite elements for the approximation of the domain and primary variables and another mesh of control domains, which also covers the whole domain, to satisfy the governing differential equations are used. The approach is distinguished from both the finite element method and the finite volume method, although the method shares the desirable features of both methods. Numerical examples are presented to illustrate the methodology and accuracy compared to the finite element and finite volume solutions.An averaging scheme for the efficient approximation of time-periodic flow problemshttps://zbmath.org/1521.763622023-11-13T18:48:18.785376Z"Richter, Thomas"https://zbmath.org/authors/?q=ai:richter.thomas|richter.thomas-michaelSummary: We study periodic solutions to the Navier-Stokes equations. The transition phase of a dynamic Navier-Stokes solution to the periodic-in-time state can be excessively long and it depends on parameters like the domain size and the viscosity. Several methods for an accelerated identification of the correct initial data that will yield the periodic state exist. They are mostly based on space-time frameworks for directly computing the periodic state or on optimization schemes or shooting methods for quickly finding the correct initial data that yields the periodic solution. They all have a large computational overhead in common. Here we describe and analyze a simple averaging scheme that comes at negligible additional cost. We numerically demonstrate the efficiency and robustness of the scheme for several test-cases and we will theoretically show convergence for the linear Stokes problem.Skeleton-stabilized divergence-conforming B-spline discretizations for incompressible flow problems of high Reynolds numberhttps://zbmath.org/1521.763702023-11-13T18:48:18.785376Z"Tong, Guoxiang Grayson"https://zbmath.org/authors/?q=ai:tong.guoxiang-grayson"Kamensky, David"https://zbmath.org/authors/?q=ai:kamensky.david"Evans, John A."https://zbmath.org/authors/?q=ai:evans.john-aSummary: We consider a stabilization method for divergence-conforming B-spline discretizations of the incompressible Navier-Stokes problem wherein jumps in high-order normal derivatives of the velocity field are penalized across interior mesh facets. We prove that this method is pressure robust, consistent, and energy stable, and we show how to select the stabilization parameter appearing in the method so that excessive numerical dissipation is avoided in both the cross-wind direction and in the diffusion-dominated regime. We examine the efficacy of the method using a suite of numerical experiments, and we find the method yields optimal \(\mathbf{L}^2\) and \(\mathbf{H}^1\) convergence rates for the velocity field, eliminates spurious small-scale structures that pollute Galerkin approximations, and is effective as an Implicit Large Eddy Simulation (ILES) methodology.Artificial compressibility approaches in flux reconstruction for incompressible viscous flow simulationshttps://zbmath.org/1521.763712023-11-13T18:48:18.785376Z"Trojak, W."https://zbmath.org/authors/?q=ai:trojak.will"Vadlamani, N. R."https://zbmath.org/authors/?q=ai:vadlamani.nagabhushana-rao"Tyacke, J."https://zbmath.org/authors/?q=ai:tyacke.james-c"Witherden, F. D."https://zbmath.org/authors/?q=ai:witherden.freddie-d"Jameson, A."https://zbmath.org/authors/?q=ai:jameson.antonySummary: Artificial compressibility methods intend to offer divergence-free free velocity fields at the incompressible limit for compressible solvers. Three major approaches for this are compared within a high-order flux reconstruction framework: the established method (ACM) of \textit{A. J. Chorin} [J. Comput. Phys. 2, 12--26 (1967; Zbl 0149.44802)] and a new entropically damped method (EDAC) of \textit{J. R. Clausen} [``Entropically damped form of artificial compressibility for explicit simulation of incompressible flow'', Phys. Rev. E (3) 87, No. 1, Article ID 013309, 12 p. (2013; \url{doi:10.1103/physreve.87.013309})] which can keep velocity divergence sufficiently low to be run explicitly without the non-linear solver required by ACM. Furthermore, the ACM approach with hyperbolised diffusion is investigated. The accuracy and computational efficiency of these methods is investigated for a series of turbulent test cases over a range of Reynolds numbers. It is found for EDAC that velocity divergence scales linearly with the square root of compressibility, whereas for ACM a clear relation is not observed. EDAC is found to accurately resolve the low Reynolds number Taylor-Green vortex case; however, for the circular cylinder at Reynolds number 3900, earlier transition of the free shear-layer is observed due to an over-production of the turbulence kinetic energy. This over production of turbulent kinetic energy is attributed to the increased spatial pressure gradients of the EDAC method, and similar behaviour is observed for an aerofoil at Reynolds number \(60\, 000\) with an attached transitional boundary layer. These issues were not observed for the other ACM approaches. It is concluded that hyperbolic diffusion of ACM can be beneficial in terms of convergence but at the cost of case setup time, and EDAC can be a time efficient method for unsteady incompressible flows. However, care must be taken when reducing the stiffness of EDAC as the resulting pressure fluctuations can have a significant impact on transition.Unfitted finite element methods based on correction functions for Stokes flows with singular forces of low regularityhttps://zbmath.org/1521.763852023-11-13T18:48:18.785376Z"Zhang, Qian"https://zbmath.org/authors/?q=ai:zhang.qian.14|zhang.qian.2|zhang.qian.3"Ji, Haifeng"https://zbmath.org/authors/?q=ai:ji.haifeng"Liang, Dong"https://zbmath.org/authors/?q=ai:liang.dong.1|liang.dongSummary: This paper presents an unfitted finite element method based on correction functions for solving stationary Stokes flows with singular forces acting on an immersed interface. It has been shown that the singular force is equivalent to a nonhomogeneous jump condition on the interface. In this paper, we consider the case that the jump has a low regularity so that it is impossible to use pointwise values on the interface to construct correction functions, as done in [\textit{J. Guzmán} et al., Math. Comput. 85, No. 301, 2071--2098 (2016; Zbl 1342.65218)]. The natural way to deal with the problem is to use mean values of the jump on the parts of the interface cut by elements, instead of using pointwise values. However, we show that it may cause instability and the constant in the error estimate may depend on the interface location relative to the mesh. Inspired by \textit{R. Guo} and \textit{T. Lin} [SIAM J. Numer. Anal. 57, No. 4, 1545--1573 (2019; Zbl 1420.65122)], we use a larger fictitious circle to overcome these issues. Associated with the correction functions, we consider two stable finite element pairs: the Mini element and the \(P_2 - P_0\) element, including the cases of continuous and discontinuous pressures. The optimal approximation capabilities of the correction functions and optimal error estimates of the finite element methods are both derived with a hidden constant independent of the interface location relative to the mesh. Numerical examples are provided to validate the theoretical results.A mass-momentum consistent, volume-of-fluid method for incompressible flow on staggered gridshttps://zbmath.org/1521.763912023-11-13T18:48:18.785376Z"Arrufat, T."https://zbmath.org/authors/?q=ai:arrufat.t"Crialesi-Esposito, M."https://zbmath.org/authors/?q=ai:crialesi-esposito.marco"Fuster, D."https://zbmath.org/authors/?q=ai:fuster.daniel"Ling, Y."https://zbmath.org/authors/?q=ai:ling.yue|ling.yonghui|ling.yunhao|ling.yonggen|ling.yuting|ling.yan|ling.you|ling.yin|ling.yunzhi|ling.yunxiang|ling.yinsheng|ling.youzhu|ling.yurong|ling.yun|ling.yingjian|ling.yingju|ling.yuesheng|ling.yibei|ling.yanyan|ling.yaobin|ling.yongshun|ling.yi|ling.yonghong|ling.yongyong|ling.yongfa|ling.yihong"Malan, L."https://zbmath.org/authors/?q=ai:malan.l"Pal, S."https://zbmath.org/authors/?q=ai:pal.shanoli-samui|pal.samarendranath|pal.surya-kant|pal.sankar-kumar|pal.soumyabrata|pal.shubhraj|pal.saheb|pal.souvik|pal.subhadip|pal.subhas-chandra|pal.suvra|pal.sumana|pal.subhabaha|pal.subrata|pal.sukla|pal.satyabrata|pal.surajit|pal.shilpa|pal.sudebkumar-prasant|pal.satrajit|pal.suryakanta|pal.samaras|pal.sat|pal.santinath|pal.sudipta-kumar|pal.s-g|pal.srimanta|pal.subahdip|pal.shankar|pal.soham|pal.swadesh|pal.subhajyoti|pal.shish|pal.sayan-kumar|pal.shukla|pal.samaresh|pal.shesansu-sekhar|pal.sankar-kr|pal.swapan-kr|pal.sanghamitra|pal.soumyasundar|pal.surjya-k|pal.siddharth|pal.sitaram|pal.sukhomay|pal.supriya-n|pal.santi-ranjan|pal.sarbajit|pal.soumitra|pal.sonia|pal.smita|pal.shreya|pal.subham|pal.suvajit|pal.sanjit|pal.sanchari|pal.sarmistha|pal.soumen|pal.sagartanu|pal.surojit|pal.santu|pal.sandip-kumar|pal.subha|pal.shiv-kumar|pal.sarbeswar|pal.supratik|pal.susovan|pal.soumik|pal.sudip-kumar|pal.saibal-kumar|pal.sridip|pal.saikat|pal.shyamosree|pal.sujata|pal.soumyadeep|pal.suchetana|pal.sandor|pal.sushma|pal.samarandranath|pal.subhajit|pal.sourav.1|pal.sagarika"Scardovelli, R."https://zbmath.org/authors/?q=ai:scardovelli.ruben"Tryggvason, G."https://zbmath.org/authors/?q=ai:tryggvason.gretar"Zaleski, S."https://zbmath.org/authors/?q=ai:zaleski.stephaneSummary: The computation of flows with large density contrasts is notoriously difficult. To alleviate the difficulty we consider a discretization of the Navier-Stokes equation that advects mass and momentum in a consistent manner. Incompressible flow with capillary forces is modeled and the discretization is performed on a staggered grid of Marker and Cell type. The Volume-of-Fluid method is used to track the interface and a Height-Function method is used to compute surface tension. The advection of the volume fraction is performed using either the Lagrangian-Explicit / CIAM (Calcul d'Interface Affine par Morceaux) method or the Weymouth and Yue (WY) Eulerian-Implicit method. The WY method conserves fluid mass to machine accuracy provided incompressibility is satisfied. To improve the stability of these methods momentum fluxes are advected in a manner ``consistent'' with the volume-fraction fluxes, that is a discontinuity of the momentum is advected at the same speed as a discontinuity of the density. To find the density on the staggered cells on which the velocity is centered, an auxiliary reconstruction of the density is performed. The method is tested for a droplet without surface tension in uniform flow, for a droplet suddenly accelerated in a carrying gas at rest at very large density ratio without viscosity or surface tension, for the Kelvin-Helmholtz instability, for a 3mm-diameter falling raindrop and for an atomizing flow in air-water conditions.Effects of cell quality in grid boundary layer on the simulated flow around a square cylinderhttps://zbmath.org/1521.764012023-11-13T18:48:18.785376Z"Bruno, Luca"https://zbmath.org/authors/?q=ai:bruno.luca"Oberto, Davide"https://zbmath.org/authors/?q=ai:oberto.davideSummary: The flow around a square cylinder is widely studied as a paradigmatic case in bluff body aerodynamics. The effects of several physical parameters of the setup, and the errors induced by turbulence models, numerical schemes and grid density have been emphasized in a huge number of studies during the past two decades. Surprisingly, the effects of the grid quality on such a class of flow has been overlooked. The lack of a shared approach and suggested best practices for high-quality grid generation among scholars and practitioners follows. The present study aims at filling this gap. The cell skewness and non-orthogonality are adopted as metrics of the grid quality. The errors induced by poor quality cells and the possible corrective measures are discussed in a Finite Volume Method framework. The effects of the cell quality on the simulated flow are systematically evaluated by a parametrical study including four different types of grid boundary layer. The obtained results are compared among them and discussed in terms of instantaneous and time-averaged flow fields, stress distribution at wall, and aerodynamic coefficients. Both the overall modelling error and the skewness-induced one are evaluated with reference to a huge number of data collected from previous studies. The local error induced by few, moderately skewed, near-wall cells upwind the cylinder propagates windward because of the convection-dominated problem, and globally affects the boundary layer separation and the vortex shedding in the wake. Skewness around the trailing edge only affects the flow to a lower extent. The skewness error on bulk aerodynamic coefficients may largely prevails on the overall modelling error, in spite of the very simple turbulence model deliberately adopted in the study. Hybrid grid boundary layer made of structured cells along the cylinder sides and unstructured ones around its edges provides results analogous to the ones obtained with a fully orthogonal grid, in spite of some clusters of few skewed cells far from the wall. Hybrid grid boundary layer is recommended as a fine balance between accuracy and flexibility in grid generation, when full orthogonal grid boundary layer is not feasible around real-world engineering applications having complicate geometries with multiple obtuse or acute edges.Assessment of a point-cloud volume-of-fluid method with sharp interface advectionhttps://zbmath.org/1521.764042023-11-13T18:48:18.785376Z"Castello Branco, Rodrigo L. F."https://zbmath.org/authors/?q=ai:castello-branco.rodrigo-l-f"Kassar, Bruno B. M."https://zbmath.org/authors/?q=ai:kassar.bruno-b-m"Carneiro, João N. E."https://zbmath.org/authors/?q=ai:carneiro.joao-n-e"Nieckele, Angela O."https://zbmath.org/authors/?q=ai:nieckele.angela-oSummary: Multiphase flows are ubiquitous in nature and industry. In order to fully describe multiphase systems, simulation approaches must be able to handle the interfaces separating the different phases properly. The Volume of Fluid (VOF) approach is widely used by researchers and engineers due to its intrinsic ability to conserve volume and handle large interface topology changes. A common problem that occurs in VOF Methods relates to the calculation of interfacial tension forces in the momentum equations while resolving a sharp interface. Common methods based on the gradients of the volume fraction field may lack accuracy due to the curvature and normal vector estimates through an abrupt transition. To address these points, the present work introduces a new proposal, where the VOF method based on a cloud of points for interface curvatures computation (PC-VOF) is extended by the coupling with the sharp-interface advection algorithm \texttt{isoAdvector}, implemented in the open source suite OpenFOAM{\circledR}. The coupled method performs better than the ones implemented in the original solvers in a number of benchmark cases from the literature. It is shown to significantly reduce the spurious currents and also presents more stable and accurate results, especially for irregular triangular meshes.Stratified flow past a sphere at moderate Reynolds numbershttps://zbmath.org/1521.764092023-11-13T18:48:18.785376Z"Cocetta, Francesco"https://zbmath.org/authors/?q=ai:cocetta.francesco"Gillard, Mike"https://zbmath.org/authors/?q=ai:gillard.mike"Szmelter, Joanna"https://zbmath.org/authors/?q=ai:szmelter.joanna"Smolarkiewicz, Piotr K."https://zbmath.org/authors/?q=ai:smolarkiewicz.piotr-kSummary: A numerical study of stably stratified flows past spheres at Reynolds numbers \(R e = 200\) and \(R e = 300\) is reported. In these flow regimes, a neutrally stratified laminar flow induces distinctly different near-wake features. However, the flow behaviour changes significantly as the stratification increases and suppresses the scale of vertical displacements of fluid parcels. Computations for a range of Froude numbers \(F r \in [ 0.1 , \infty ]\) show that as Froude number decreases, the flow patterns for both Reynolds numbers become similar. The representative simulations of the lee-wave instability at \(F r = 0.625\) and the two-dimensional vortex shedding at \(F r = 0.25\) regimes are illustrated for flows past single and tandem spheres, thereby providing further insight into the dynamics of stratified flows past bluff bodies. In particular, the reported study examines the relative influence of viscosity and stratification on the dividing streamline elevation, wake structure and flow separation. The solutions of the Navier-Stokes equations in the incompressible Boussinesq limit are obtained on unstructured meshes suitable for simulations involving multiple bodies. Computations are accomplished using the finite volume, non-oscillatory forward-in-time (NFT) Multidimensional Positive Definite Transport Algorithm (MPDATA) based solver. The impact and validity of the numerical approximations, especially for the cases exhibiting strong stratification, are also discussed. Qualitative and quantitative comparisons with available laboratory experiments and prior numerical studies confirm the validity of the numerical approach.An enhancement of coupling method for interface computations in incompressible two-phase flowshttps://zbmath.org/1521.764152023-11-13T18:48:18.785376Z"Duy, Trong-Nguyen"https://zbmath.org/authors/?q=ai:duy.trong-nguyen"Nguyen, Van-Tu"https://zbmath.org/authors/?q=ai:nguyen.van-tu"Phan, Thanh-Hoang"https://zbmath.org/authors/?q=ai:phan.thanh-hoang"Park, Warn-Gyu"https://zbmath.org/authors/?q=ai:park.warn-gyuSummary: Coupling techniques that take advantage of the mass conservation property of the volume-of-fluid (VOF) method and the sharpened interface computation of the Level Set (LS) approach are widely used for computations with high accuracy order demands. In this paper, an enhanced coupling method for interface computations in incompressible two-phase flows is presented. In the proposed method, the solution of the re-initialization LS function is reformulated in a conservative form before it is applied to estimate the interface curvature and interface normal vector. The estimated interface exhibits significant improvements in smoothness and accuracy compared to those obtained with the original VOF method and a previous coupling method. The proposed method is then implemented in an incompressible Navier-Stokes solver (interFoam) in the OpenFOAM platform to solve several benchmark tests. Good agreement between the simulated results and the analytical/benchmark solutions with well-preserved mass conservation is obtained for standard tests, including a reversed single vortex, static droplet, and rising bubble, thus demonstrating the potential of the proposed technique for both academic research and practical applications.A discrete adjoint method for pressure-based algorithmshttps://zbmath.org/1521.764202023-11-13T18:48:18.785376Z"Fleischli, Benno"https://zbmath.org/authors/?q=ai:fleischli.benno"Mangani, Luca"https://zbmath.org/authors/?q=ai:mangani.luca"Del Rio, Armando"https://zbmath.org/authors/?q=ai:del-rio.armando"Casartelli, Ernesto"https://zbmath.org/authors/?q=ai:casartelli.ernestoSummary: A discrete adjoint method implemented in a coupled pressure-based RANS solver is presented in this paper. The adjoint equations are solved using an adjoint fixed point iteration that inherits the convergence properties of the primal solver. Automatic differentiation is used extensively for the construction of the adjoint fixed point iteration. The concept of Krylov subspace methods was adopted to stabilize the solution procedure. A common linearization technique in collocated pressure-based algorithms is the introduction of a mass flux variable on the cell faces which is kept constant during the inner iterations. This variable is treated as an independent adjoint variable in related publications. We propose a new method that allows to treat the mass fluxes implicitly in order to take full advantage of the preconditioner of the primal solver. The adjoint solver is general and is not restricted by the commonly used frozen turbulence approximation. It can deal with any turbulence model that is supported by the flow solver as well as any boundary condition. This includes mixing planes and mesh interfaces needed for multi stage turbo machinery simulations. Furthermore, there is no restriction on the choice of objective function. The sensitivities of the adjoint solver have been validated with sensitivities obtained with finite differences. An entirely surface based interpolation method based on radial basis functions (RBF) was developed to deform the surface mesh. We propose the use of discrete geodesics instead of the classical Euclidean distance as the distance measure for the RBF interpolation. As an alternative, a direct deformation method with adjoint consistent smoothing is also described and used in the presented optimization cases. The developed adjoint solver and deformation routines were used to optimize a turbulent bend with different Reynolds numbers as well as the the rotor blade of an axial turbine.Multirate partitioned Runge-Kutta methods for coupled Navier-Stokes equationshttps://zbmath.org/1521.764342023-11-13T18:48:18.785376Z"Kang, Shinhoo"https://zbmath.org/authors/?q=ai:kang.shinhoo"Dener, Alp"https://zbmath.org/authors/?q=ai:dener.alp"Hamilton, Aidan"https://zbmath.org/authors/?q=ai:hamilton.aidan"Zhang, Hong"https://zbmath.org/authors/?q=ai:zhang.hong.2"Constantinescu, Emil M."https://zbmath.org/authors/?q=ai:constantinescu.emil-m"Jacob, Robert L."https://zbmath.org/authors/?q=ai:jacob.robert-lSummary: Earth system models are complex integrated models of atmosphere, ocean, sea ice, and land surface. Coupling the components can be a significant challenge due to the difference in physics, temporal, and spatial scales. This study explores multirate partitioned Runge-Kutta methods for the fluid-fluid interaction problem and demonstrates its parallel performance by using the PETSc library. We consider compressible Navier-Stokes equations with gravity coupled through a rigid-lid interface. Our large-scale numerical experiments reveal that multirate partitioned Runge-Kutta coupling schemes (1) can conserve total mass; (2) have second-order accuracy in time; and (3) provide favorable strong- and weak-scaling performance on modern computing architectures. We also show that the speedup factors of multirate partitioned Runge-Kutta methods match theoretical expectations over their base (single-rate) method.A symmetry-preserving second-order time-accurate PISO-based methodhttps://zbmath.org/1521.764352023-11-13T18:48:18.785376Z"Komen, E. M. J."https://zbmath.org/authors/?q=ai:komen.e-m-j"Hopman, J. A."https://zbmath.org/authors/?q=ai:hopman.j-a"Frederix, E. M. A."https://zbmath.org/authors/?q=ai:frederix.edo-m-a"Trias, F. X."https://zbmath.org/authors/?q=ai:trias.francesc-xavier"Verstappen, R. W. C. P."https://zbmath.org/authors/?q=ai:verstappen.r-w-c-pSummary: A new conservative symmetry-preserving second-order time-accurate PISO-based pressure-velocity coupling for solving the incompressible Navier-Stokes equations on unstructured collocated grids is presented in this paper. This new method for implicit time stepping is an extension of the conservative symmetry-preserving incremental-pressure projection method for explicit time stepping and unstructured collocated meshes of Trias et al. [35]. In order to assess and compare both methods, we have implemented them within one unified solver in the open source code OpenFOAM where we use a Butcher array to prescribe the Runge-Kutta method. Thus, by changing the entries of the Butcher array, explicit and diagonally implicit Runge-Kutta schemes can be combined into one solver. We assess the energy conservation properties of the implemented discretisation methods and the temporal consistency of the selected Runge-Kutta schemes using Taylor-Green vortex and lid-driven cavity flow test cases. Finally, we use a more complex turbulent channel flow test case in order to further assess the performance of the presented new conservative symmetry-preserving incremental-pressure PISO-based method.
Although both implemented methods are based on a symmetry-preserving discretisation, we show they still produce a small amount of numerical dissipation when the total pressure is directly solved from a Poisson equation. When an incremental-pressure approach is used, where a pressure correction is solved from a Poisson equation, both methods are effectively fully-conservative. For high-fidelity simulations of incompressible turbulent flows, it is highly desirable to use fully-conservative methods. For such simulations, the presented numerical methods are therefore expected to have large added value, since they pave the way for the execution of truly energy-conservative high-fidelity simulations in complex geometries. Furthermore, both methods are implemented in OpenFOAM, which is widely used within the CFD community, so that a large part of this community can benefit from the developed and implemented numerical methods.Influence of sidewalls on three-dimensional turbulent wall jet: an experimental and numerical approachhttps://zbmath.org/1521.764382023-11-13T18:48:18.785376Z"Kumar, Sarvesh"https://zbmath.org/authors/?q=ai:kumar.sarvesh"Kumar, Amitesh"https://zbmath.org/authors/?q=ai:kumar.amiteshSummary: In this study, with the help of with and without sidewall configurations, experimental and numerical approaches are utilised to investigate the sidewall influence on a three-dimensional turbulent wall jet. The mean flow profile of the three-dimensional turbulent wall jet is measured through experimental method and compared with the numerical results. In addition, the numerical method is used to characterise the turbulence characteristics of the wall jet for both the configurations. A 200 mm square nozzle (height \(h=20 \pm 0.5\) mm) is used to generate the developing jet exit profile for the experimental results. The Reynolds number based on the jet exit velocity and nozzle height is 25,000. The numerical results are obtained by solving the Reynolds Average Navier stokes (RANS) equations with low Reynolds number \(k\)-\(\varepsilon\) turbulence models proposed by Yang and Shih and Launder and Sharma. The experimental results are obtained by a single probe hotwire anemometer and a K-type thermocouple. It is observed that the sidewall affects the temperature distribution just after the potential core region \((x/h = 5\)) whereas the velocity distribution is affected in the fully developed region after the downstream location \(x/h = 22.5\). Sidewalls drastically influenced the thermal and velocity decay in wall-normal and lateral directions. It is found from the numerical simulation that the decay of maximum streamwise velocity is increased by 9\%, whereas centerline temperature decay is decreased by 25\% in sidewall configuration as compared to without sidewall configuration. The contour plots of temperature and velocity also exhibit the sidewall effect on the whole domain. The Reynolds shear stress \(<u^\prime v^\prime>\) dominates in the vertical jet centerline plane (at \(z = 0\)), whereas \(< u^\prime w^\prime >\) dominates in the lateral direction at \(y_{max}\) plane in both the configurations. On the vertical jet centerline plane (at \(z = 0\)), Reynolds shear stress \(<u^\prime v^\prime>\) is nearly increased by 10\% in the presence of sidewall compared to without sidewall configuration. The entrainment of the ambient fluid initially decreases, but after the downstream location \(x/h = 22.4\), it increases for the case of the sidewall compared to the corresponding case without the sidewall. This happens owing to an increase in maximum turbulent kinetic energy generation inside the flow domain by 10\%. The turbulent heat flux \(<T^\prime V^\prime>\) dominates in lateral and wall-normal shear layers in both the configurations. The correlations of decay of temperature and velocity are also suggested through numerical techniques.A robust hybrid unstaggered central and Godunov-type scheme for Saint-Venant-Exner equations with wet/dry frontshttps://zbmath.org/1521.764412023-11-13T18:48:18.785376Z"Li, Dingfang"https://zbmath.org/authors/?q=ai:li.dingfang"Dong, Jian"https://zbmath.org/authors/?q=ai:dong.jianSummary: We aim to propose a robust hybrid unstaggered central and Godunov-type scheme based on hydrostatic reconstruction (HR) for Saint-Venant-Exner equations with wetting and drying transitions. The discretization of the bed slope source term is based on the HR method to preserve the still water steady-state solution. The hydrodynamic model described by the Saint-Venant system is numerically solved using the well-balanced unstaggered central scheme proposed in [\textit{J. Dong} and \textit{D. F. Li}, Appl. Math. Comput. 372, Article ID 124992, 18 p. (2020; Zbl 1433.76105)]. The morphodynamic model described by the Exner equation is numerically solved by using a Lax-Friedrichs method. In solving the morphodynamic model, we proposed a novel ``cut-off'' function to guarantee the nonlinear stability and preserve the stationary solution. The present scheme can exactly obtain the stationary solution and is capable of guaranteeing the positivity of the water depth. The key contributions of this work are the well-balanced property at the wet-dry fronts and the stability of the current scheme in solving two physical models that have relatively either strong or weak interactions. Finally, we use several classical problems of the system to demonstrate these properties.Hybrid particle-grid methods for the study of differential diffusion in turbulent flowshttps://zbmath.org/1521.764642023-11-13T18:48:18.785376Z"Santoso, Simon"https://zbmath.org/authors/?q=ai:santoso.simon"Lagaert, Jean-Baptiste"https://zbmath.org/authors/?q=ai:lagaert.jean-baptiste"Balarac, Guillaume"https://zbmath.org/authors/?q=ai:balarac.guillaume"Cottet, Georges-Henri"https://zbmath.org/authors/?q=ai:cottet.georges-henriSummary: This paper is devoted to the development and application of hybrid methods combining, on the one hand, semi-lagrangian methods for the advection-diffusion of scalars, and, on the other hand, either finite volume or spectral methods, depending on the flow geometry, for the Navier-Stokes equations. A particular focus is made on the accuracy and scalability of the methods. These methods are then used to study differential diffusion of scalars on two canonical cases: Homogeneous Isotropic Turbulence and a jet flow. We first characterize differential diffusion in terms of spectral distribution. We then use the Reynolds decomposition to bring out the different mechanisms involved in the energy budget of the scalar and we analyze their spatial distribution.CFD-based shape optimization under uncertainties using the adjoint-assisted polynomial chaos expansion and projected derivativeshttps://zbmath.org/1521.764672023-11-13T18:48:18.785376Z"Skamagkis, Th."https://zbmath.org/authors/?q=ai:skamagkis.th"Papoutsis-Kiachagias, E. M."https://zbmath.org/authors/?q=ai:papoutsis-kiachagias.evangelos-m"Giannakoglou, K. C."https://zbmath.org/authors/?q=ai:giannakoglou.kyriakos-cSummary: This paper is dealing with gradient-based optimization in fluid mechanics, in the presence of uncertainties, by focusing on turbulent flows governed by the RANS equations. Uncertainty Quantification (UQ) is performed using the First-Order Second-Moment (FOSM) method and the more accurate Adjoint-assisted (non-intrusive) Polynomial Chaos Expansion (APCE); in the latter, first-order derivatives of the Quantity of Interest (QoI) with respect to the uncertain variables, provided by the adjoint method, are used to reduce the cost for computing the polynomial coefficients. Both methods compute the first two statistical moments (mean value and standard deviation of the QoI) and the objective function to be optimized is their weighted sum. Gradient-based optimization with such an objective function requires mixed derivatives of the QoI with respect to the design and uncertain variables. In adjoint-based optimization, one way to compute these derivatives is by solving the systems of PDEs resulting from the differentiation of the flow and adjoint equations with respect to the uncertain variables, at a cost that scales with their number. To reduce the CPU cost, the objective function gradient can be expressed in terms of the projection of the mixed derivatives' matrix onto vectors. Such projections are herein utilized with both the aforementioned UQ methods, in the context of robust design optimization. Firstly, the projected FOSM method, presented for laminar flows in a previous article by the same group, is extended to turbulent flows solved using the Spalart-Allmaras model by including its adjoint. Then, the projected APCE method is developed, programmed and tested for the first time in the literature. In both pFOSM and pAPCE, the cost for computing the projected matrix of mixed derivatives does not scale with the number of either the design or the uncertain variables. Both methods are implemented within the \textit{adjointOptimisation} library of OpenFOAM, which makes use of the continuous adjoint method, and are demonstrated in the aerodynamic shape optimization of airfoils, in laminar and turbulent flows.Immersed boundary method for the incompressible Reynolds averaged Navier-Stokes equationshttps://zbmath.org/1521.764752023-11-13T18:48:18.785376Z"Troldborg, Niels"https://zbmath.org/authors/?q=ai:troldborg.niels"Sørensen, Niels N."https://zbmath.org/authors/?q=ai:sorensen.niels-n"Zahle, Frederik"https://zbmath.org/authors/?q=ai:zahle.frederikSummary: This paper presents an immersed boundary method for the incompressible Reynolds Averaged Navier-Stokes equations using the \(k-\omega-SST\) turbulence model and two different wall functions to approximate the near wall flow. The main focus of the paper is to address a range of numerical issues related to the implementation of the method and to describe in detail how to implement it in a finite volume code. The boundary conditions for the governing equations at the immersed boundary are imposed in a manner which is consistent with their treatment on a standard body conforming grid. The method is verified and validated by simulating a NACA 0012 airfoil at a Reynolds number of \(Re=6\cdot 10^6\). The results confirm that the implementations are stable even on very coarse grids, however, in contrast to what is reported elsewhere in the literature, the predicted lift and drag of the airfoil are not necessarily improved by using a wall function which assumes a linear near wall velocity instead of a standard logarithmic velocity profile.
Finally, the method is applied to the flow past a tree and shown to be able to make drag predictions, which are in good agreement with wind tunnel measurements.An immersed boundary approach for high order weighted essentially non-oscillatory schemeshttps://zbmath.org/1521.765362023-11-13T18:48:18.785376Z"Di Mascio, Andrea"https://zbmath.org/authors/?q=ai:di-mascio.andrea"Zaghi, Stefano"https://zbmath.org/authors/?q=ai:zaghi.stefanoSummary: A new immersed boundary approach for high order Weighted Essentially non-Oscillatory (WENO) schemes is proposed. The schemes is based on the main ideas from both the general immersed boundary algorithms and the level-set approach and can be easily applied to both finite difference and finite volume formulation. Although formally only second order accurate, numerical tests prove that the use of higher order approximation for the Eulerian fluxes can be very convenient to capture flow details and to obtain low uncertainty also with very coarse grids.An Eulerian-based immersed boundary method for particle suspensions with implicit lubrication modelhttps://zbmath.org/1521.765422023-11-13T18:48:18.785376Z"Hori, Naoki"https://zbmath.org/authors/?q=ai:hori.naoki"Rosti, Marco E."https://zbmath.org/authors/?q=ai:rosti.marco-edoardo|rosti.marco-edorardo"Takagi, Shu"https://zbmath.org/authors/?q=ai:takagi.shuSummary: We describe an immersed boundary method in which the fluid-structure coupling is achieved in an Eulerian framework. The method is an improved extension of the immersed boundary method originally developed by \textit{T: Kajishima} et al. [``Turbulence structure of particle-laden flow in a vertical plane channel due to vortex shedding'', JSME Int. J. Ser. B, Fluids Therm. Eng. 44, 4, 526--535 (2001; \url{doi:10.1299/jsmeb.44.526})], which accounts for the inertia of the fictitious fluid inside the particle volume and is thus able to reproduce the behavior of particles both in the case of neutrally-buoyant objects and in the presence of density difference between the particles and the fluid. The method is capable to handle the presence of multiple suspended objects, i.e., a suspension, by including a soft-sphere normal collision model, while the lubrication correction typically added to similar immersed boundary methods in order to capture the sub-grid unresolved lubrication force is here treated implicitly, i.e., naturally obtained without any explicit expression, thus no additional computation is required. We show that our methodology can successfully reproduce the rheology of a particle suspension in a shear flow up to a dense regime (with a maximum particle volume fraction around 46\%) without any additional correction force. The applicability of this methodology is also tested in a turbulent pressure-driven duct flow at high Reynolds number in the presence of non-negligible inertia and non-uniform shear-rate, showing good agreement with experimental measurements.Direct numerical simulations of the swirling von Kármán flow using a semi-implicit moving immersed boundary methodhttps://zbmath.org/1521.765482023-11-13T18:48:18.785376Z"Kasbaoui, M. Houssem"https://zbmath.org/authors/?q=ai:kasbaoui.m-houssem"Kulkarni, Tejas"https://zbmath.org/authors/?q=ai:kulkarni.tejas-d"Bisetti, Fabrizio"https://zbmath.org/authors/?q=ai:bisetti.fabrizioSummary: We present a novel moving immersed boundary method (IBM) and employ it in direct numerical simulations (DNS) of the closed-vessel swirling von Kármán flow in laminar and turbulent regimes. The IBM extends direct-forcing approaches by leveraging a time integration scheme, that embeds the immersed boundary forcing step within a semi-implicit iterative Crank-Nicolson scheme. The overall method is robust, stable, and yields excellent results in canonical cases with static and moving boundaries. The moving IBM allows us to reproduce the geometry and parameters of the swirling von Kármán flow experiments in
[\textit{F. Ravelet} et al., J. Fluid Mech. 601, 339--364 (2008; Zbl 1151.76344)])
on a Cartesian grid. In these DNS, the flow is driven by two-counter rotating impellers fitted with curved inertial stirrers. We analyze the transition from laminar to turbulent flow by increasing the rotation rate of the counter-rotating impellers to attain the four Reynolds numbers 90, 360, 2000, and 4000. In the laminar regime at Reynolds number 90 and 360, we observe flow features similar to those reported in the experiments and in particular, the appearance of a symmetry-breaking instability at Reynolds number 360. We observe transitional turbulence at Reynolds number 2000. Fully developed turbulence is achieved at Reynolds number 4000. Non-dimensional torque computed from simulations matches correlations from experimental data. The low Reynolds number symmetries, lost with increasing Reynolds number, are recovered in the mean flow in the fully developed turbulent regime, where we observe two tori symmetrical about the mid-height plane. We note that turbulent fluctuations in the central region of the device remain anisotropic even at the highest Reynolds number 4000, suggesting that isotropization requires significantly higher Reynolds numbers.Direct simulation of two-dimensional Bénard flow with free-slip boundary conditionshttps://zbmath.org/1521.765782023-11-13T18:48:18.785376Z"Rodakoviski, Rodrigo"https://zbmath.org/authors/?q=ai:rodakoviski.rodrigo"Dias, Nelson L."https://zbmath.org/authors/?q=ai:dias.nelson-lSummary: A fourth-order finite difference algorithm is developed for the direct simulation of two-dimensional Rayleigh-Bénard convection in a horizontally periodic domain of aspect ratio \(\Gamma\). The free-slip condition prevents the formation of kinetic boundary layers and allow the implementation of an efficient long-stencil scheme for the vorticity equation without additional risk of instability. The required grid size to properly resolve Batchelor's microscale and therefore avoid aliasing is expressed in terms of the Rayleigh (Ra) and Prandtl (Pr) numbers. It was verified that the method was able to reproduce the Nusselt and Reynolds number scalings as well as the different flow regimes documented in the literature for \(\Gamma = 5\), \(\operatorname{Pr} = 10\), and \(\operatorname{Ra} \leq 10^7\). Furthermore, the analytical solution of the Poisson equation in Fourier series is derived and compared with the standard fast Poisson solver. The horizontal wavenumbers decay much slower than the vertical ones, which might be explained by the adopted domain's aspect ratio. The results also suggest that the largest energy-containing wavenumbers scale with \(\operatorname{Ra}^{3 / 8}\) for large enough Rayleigh numbers.Fourth order compact scheme for the Navier-Stokes equations on time deformable domainshttps://zbmath.org/1521.765872023-11-13T18:48:18.785376Z"Sen, Shuvam"https://zbmath.org/authors/?q=ai:sen.shuvam"Sheu, Tony W. H."https://zbmath.org/authors/?q=ai:sheu.tony-wen-hannSummary: In this work, we report the development of a spatially fourth order temporally second order compact scheme for incompressible Navier-Stokes (N-S) equations in time-varying domain. the first author et al. [ibid. 84, 141--163 (2013; Zbl 1290.76025)] put forward an implicit compact finite difference scheme for the unsteady convection-diffusion equation. It is now further extended to simulate fluid flow problems on deformable surfaces using curvilinear moving grids. The formulation is conceptualized in conjunction with recent advances in numerical grid deformations techniques such as inverse distance weighting (IDW) interpolation and its hybrid implementation. Adequate emphasis is provided to approximate grid metrics up to the desired level of accuracy and freestream preserving property has been numerically examined. As we discretize the non-conservative form of the N-S equation, the importance of accurate satisfaction of geometric conservation law (GCL) is investigated. To the best of our knowledge, this is the first higher order compact method that can directly tackle the non-conservative form of the N-S equation in single and multi-block time dependent complex regions. Several numerical verification and validation studies are carried out to illustrate the flexibility of the approach to handle high-order approximations on evolving geometries. The method presented here is found to be effective in modeling incompressible flow on deformable domains, including situations of fluid-structure interaction (FSI). Additionally, the necessity of GCL preserving metric computation is eased as a result of the scheme's adaptation for non-conservative formulation.A generalized finite difference method for solving Stokes interface problemshttps://zbmath.org/1521.765892023-11-13T18:48:18.785376Z"Shao, Mengru"https://zbmath.org/authors/?q=ai:shao.mengru"Song, Lina"https://zbmath.org/authors/?q=ai:song.lina"Li, Po-Wei"https://zbmath.org/authors/?q=ai:li.po-weiSummary: In this paper, a new scheme is proposed to solve the Stokes interface problem. The scheme turns the Stokes interface problem into two coupled Stokes non-interface subproblems and adds a mixed boundary condition to overcome the numerical pressure oscillation. Since the interface becomes the boundary of the subproblems, the scheme has the advantage to deal with the interface problem with complex geometry. Furthermore, a generalized finite difference method (GFDM) is adopted to solve the coupled Stokes non-interface subproblems. The GFDM is developed from the Taylor series expansions and moving-least squares approximation. Due to the flexibility of the GFDM, it is convenient to handle the complex boundary conditions that appeared in the proposed scheme. The numerical examples verify the accuracy and stability of the GFDM to solve the Stokes interface problem with the mixed boundary conditions. Moreover, for some given numerical examples, the proposed scheme is more accurate than the classical formula of the pressure Poisson equation, especially in terms of pressure.A mass-conservative semi-implicit volume of fluid method for the Navier-Stokes equations with high order semi-Lagrangian advection schemehttps://zbmath.org/1521.765932023-11-13T18:48:18.785376Z"Tavelli, Maurizio"https://zbmath.org/authors/?q=ai:tavelli.maurizio"Boscheri, Walter"https://zbmath.org/authors/?q=ai:boscheri.walter"Stradiotti, Giulia"https://zbmath.org/authors/?q=ai:stradiotti.giulia"Pisaturo, Giuseppe Roberto"https://zbmath.org/authors/?q=ai:pisaturo.giuseppe-roberto"Righetti, Maurizio"https://zbmath.org/authors/?q=ai:righetti.maurizioSummary: This paper deals with the development of a semi-implicit numerical method for the Navier-Stokes equations using the non-linear volumes of fluid (VOF) approach and a semi-Lagrangian scheme for the discretization of the advection contribution based on a high order reconstruction of the velocity field. The VOF approach guarantees high flexibility and is able to reproduce several phenomena that appear in real scenarios such as free surface flows, pressurized channels and jets. The discrete velocity field from the momentum conservation law is formally inserted into the discrete continuity equation, hence yielding a mildly non-linear system for the unknown hydraulic head which can be solved through a nested Newton-type algorithm. The computation of the non-linear convective diffusion contribution is then based on a high order reconstruction of the velocity field, which is furthermore constrained to exactly recover the original pointwise values of the numerical solution. As a consequence, the mass conservation is fully preserved while providing information about the main velocity field and its high order moments, later employed in the computation of the Lagrangian trajectories needed for the discretization of the convective and diffusive terms. Furthermore, the bottom friction and the tangential stresses can be directly computed from the high order velocity reconstruction. The method is derived in a general form with the only requirement to be structured in the \(z\)-direction, so that it applies to the three- and the two-dimensional cases with unstructured grids in the horizontal space. Convergence studies are carried out to demonstrate the accuracy of the reconstruction operator. Finally, the numerical scheme is validated against several benchmarks that include \(2D_{xz}\), \(2D_{xy}\) and \(3D\) non-hydrostatic flows with complex geometry in order to show the flexibility of the proposed algorithm, including a real-world application.A novel Cahn-Hilliard-Navier-Stokes model with a nonstandard variable mobility for two-phase incompressible fluid flowhttps://zbmath.org/1521.765982023-11-13T18:48:18.785376Z"Yang, Junxiang"https://zbmath.org/authors/?q=ai:yang.junxiang"Kim, Junseok"https://zbmath.org/authors/?q=ai:kim.junseokSummary: In this study, we present a novel Cahn-Hilliard-Navier-Stokes (CHNS) system with a nonstandard variable mobility for two-phase incompressible fluid flow. Unlike the classical constant mobility, the developed variable mobility has decreasing values nearby the interface and increasing values away from the interface, which minimizes the dynamics of the Cahn-Hilliard (CH) model nearby the interface. An unconditionally stable convex splitting method is used to solve the CH equation and the projection method is used to solve the NS equation. As benchmark tests, the Rayleigh-Taylor instability, drop deformation, and rising bubble are performed to show the accuracy and practicability of the proposed model. The computational results indicate that the proposed model accurately captures the interfacial position and keeps the interface region from being too much distorted.Numerical study of incompressible binary fluids on 3D curved surfaces based on the conservative Allen-Cahn-Navier-Stokes modelhttps://zbmath.org/1521.765992023-11-13T18:48:18.785376Z"Yang, Junxiang"https://zbmath.org/authors/?q=ai:yang.junxiang"Kim, Junseok"https://zbmath.org/authors/?q=ai:kim.junseokSummary: In this article, we propose a practical and highly efficient finite difference approach for two-phase fluid simulations on three-dimensional (3D) surfaces. The hydrodynamically coupled interfacial motion is captured by using the conservative Allen-Cahn-Navier-Stokes (CACNS) equations. By adopting the closest point method and the pseudo-Neumann boundary condition, the direct computations on curved surfaces are transferred to the 3D simulations in a narrow band domain embedding the surface. The projection method with pressure correction is used to decouple the computations of velocity and pressure. The operator splitting method is used to split the calculation of conservative Allen-Cahn equation into subproblems and the nonlinear part can be analytically solved. Therefore, the whole computation in each time iteration is highly efficient and easy to implement. The numerical experiments on various 3D curved surfaces are investigated to show the good performance of the proposed method.Original variables based energy-stable time-dependent auxiliary variable method for the incompressible Navier-Stokes equationhttps://zbmath.org/1521.766002023-11-13T18:48:18.785376Z"Yang, Junxiang"https://zbmath.org/authors/?q=ai:yang.junxiang"Tan, Zhijun"https://zbmath.org/authors/?q=ai:tan.zhijun"Kim, Junseok"https://zbmath.org/authors/?q=ai:kim.junseokSummary: In this study, we develop an efficiently linear and energy-stable method for the incompressible Navier-Stokes equation. A time-dependent Lagrange multiplier is introduced to change the original equation into an equivalent form. Using the equivalent equation, we design a second-order time-accurate scheme based on the second-order backward difference formula (BDF2). The proposed scheme explicitly treats the advection term. In each time iteration, some linear elliptic type equations need to be solved. Therefore, the calculation is highly efficient. Moreover, the time-discretized energy stability with respect to original variables can be easily proved. Various benchmark tests, such as lid-driven cavity flow, Kelvin-Helmholtz instability, and Taylor-Green vortices, are performed to validate the performance of the proposed method.A ghost-cell immersed boundary method on preventing spurious oscillations for incompressible flows with a momentum interpolation methodhttps://zbmath.org/1521.766062023-11-13T18:48:18.785376Z"Zhang, Xiaohui"https://zbmath.org/authors/?q=ai:zhang.xiaohui.2|zhang.xiaohui.1|zhang.xiaohui"Gu, Xiechong"https://zbmath.org/authors/?q=ai:gu.xiechong"Ma, Ning"https://zbmath.org/authors/?q=ai:ma.ningSummary: We propose a ghost-cell immersed boundary method (GCIBM) using a local directional ghost cell approach for the simulation of incompressible flows involving solid geometry. The proposed method is based on a finite volume solver with a momentum interpolation method (MIM) on a collocated grid for the Navier-Stokes equations that is spatially discretized by a fourth-order compact scheme and temporally advanced by a fourth-order Runge-Kutta scheme. A new stencil for imposing the Neumann boundary is constructed following the least square regression. The spurious oscillations that spread from the immersed boundary are observed when the discrete momentum forcing (DMF) is obtained at the cell centers for velocities. This is due to the decoupling of the pressure and velocity fields. In this paper, the spurious oscillations are removed by the recovery of the decoupling by shifting the locations of DMF from the cell centers to the face centers. The efficiency of the proposed technique is confirmed in terms of a simulation for steady and unsteady flows with a stationary or moving geometry.A sharp interface immersed boundary method for flow-induced noise prediction using acoustic perturbation equationshttps://zbmath.org/1521.766102023-11-13T18:48:18.785376Z"Zhao, Cheng"https://zbmath.org/authors/?q=ai:zhao.cheng"Yang, Yan"https://zbmath.org/authors/?q=ai:yang.yan.4"Zhang, Tao"https://zbmath.org/authors/?q=ai:zhang.tao.25"Dong, Haibo"https://zbmath.org/authors/?q=ai:dong.haibo"Hou, Guoxiang"https://zbmath.org/authors/?q=ai:hou.guoxiangSummary: In this paper, a hybrid computational aero/hydro-acoustic approach is proposed to deal with acoustic scattering and flow-induced noise problems based on the sharp interface immersed boundary method (IBM). For the flow field, the incompressible Navier-Stokes equations are solved by an in-house direct numerical simulation solver. The acoustic field is predicted by solving acoustic perturbation equations (APEs). Both flow and acoustic solid boundaries with complexity and mobility are dealt with by the sharp interface IBM. Benchmark acoustic problems with varied scatterers in two and three dimensions are presented to validate the accuracy of the acoustic codes and boundary treatments. Then, the feasibility and accuracy of the present hybrid approach are validated by considering the problem of flow past a circular cylinder at a Reynolds number of 200. Subsequently, the present method is used to predict the noise generated by flow around a four-cylinder array in two-dimensions with two arrangements (i.e., square array and diamond array), and the flow and acoustic physics are investigated in detail. The results show that the square array retains a monopole-like sound-radiation shape, while the directivity pattern of the diamond array produces a dipole-like shape. In both the square and diamond arrays, the propagation of acoustic waves is affected by the Doppler effect, and the latter array results in a larger alternation of the propagation angle compared with the single cylinder due to the influence of the geometric configuration. The intensity of the radiated acoustic pressure is much greater for the diamond array compared to the square one in most circumferential directions, and the acoustic intensity of both arrays is greater than that of the single cylinder. The spectrums of the far-field acoustic pressure indicate that the two arrays and the single cylinder have similar peak frequencies and profiles, with vortex shedding playing the predominant role in noise generation in all three configurations.A surrogate optimization approach for inverse problems: application to turbulent mixed-convection flowshttps://zbmath.org/1521.766162023-11-13T18:48:18.785376Z"Oulghelou, M."https://zbmath.org/authors/?q=ai:oulghelou.mourad"Beghein, C."https://zbmath.org/authors/?q=ai:beghein.claudine"Allery, C."https://zbmath.org/authors/?q=ai:allery.cyrilleSummary: Optimal control of turbulent mixed-convection flows has attracted considerable attention from researchers. Numerical algorithms such as Genetic Algorithms (GAs) are powerful tools that allow to perform global optimization. These algorithms are particularly of great interest in complex optimization problems where cost functionals may lack smoothness and regularity. In turbulent flow optimization, the hybridization of GA with high fidelity Computational Fluid Dynamics (CFD) is extremely demanding in terms of computational time and memory storage. Thus, alternative approaches aiming to alleviate these requirements are of great interest. Nowadays, surrogate approaches gained attention due to their potential in predicting flow solutions based only on preexisting data. In the present paper, we propose a near-real time surrogate genetic algorithm for inverse parameter identification problems involving turbulent flows. In this optimization framework, the parameterized flow data are used in their reduced form obtained by the POD (Proper Orthogonal Decomposition) and solutions prediction is made by interpolating the temporal and the spatial POD subspaces through a recently developed Riemannian barycentric interpolation. The validation of the proposed optimization approach is carried out in the parameter identification problem of the turbulent mixed-convection flow in a cavity. The objective is to determine the inflow temperature corresponding to a given temperature distribution in a restricted area of the spatial domain. The results show that the proposed surrogate optimization framework is able to deliver good approximations of the optimal solutions within less than two minutes.Topology optimization of unsteady flows using the spectral element methodhttps://zbmath.org/1521.766182023-11-13T18:48:18.785376Z"Nobis, Harrison"https://zbmath.org/authors/?q=ai:nobis.harrison"Schlatter, Philipp"https://zbmath.org/authors/?q=ai:schlatter.philipp"Wadbro, Eddie"https://zbmath.org/authors/?q=ai:wadbro.eddie"Berggren, Martin"https://zbmath.org/authors/?q=ai:berggren.martin"Henningson, Dan S."https://zbmath.org/authors/?q=ai:henningson.dan-sSummary: We investigate the applicability of a high-order Spectral Element Method (SEM) to density based topology optimization of unsteady flows in two dimensions. Direct Numerical Simulations (DNS) are conducted relying on Brinkman penalization to describe the presence of solid within the domain. The optimization procedure uses the adjoint-variable method to compute gradients and a checkpointing strategy to reduce storage requirements. A nonlinear filtering strategy is used to both enforce a minimum length scale and to provide smoothing across the fluid-solid interface, preventing Gibbs oscillations. This method has been successfully applied to the design of a channel bend and an oscillating pump, and demonstrates good agreement with body fitted meshes. The precise design of the pump is shown to depend on the initial material distribution. However, the underlying topology and pumping mechanism is the same. The effect of a minimum length scale has been studied, revealing it to be a necessary regularization constraint for the oscillating pump to produce meaningful designs. The combination of SEM and density based optimization offer some unique challenges which are addressed and discussed, namely a lack of explicit boundary tracking exacerbated by the interface smoothing. Nevertheless, SEM can achieve equivalent levels of precision to traditional finite element methods, while requiring fewer degrees of freedom. Hence, the use of SEM addresses the two major bottlenecks associated with optimizing unsteady flows: computation cost and data storage.An implicit time spectral method using adaptive stablizationhttps://zbmath.org/1521.766192023-11-13T18:48:18.785376Z"Zhan, Lei"https://zbmath.org/authors/?q=ai:zhan.lei"Wang, Rui"https://zbmath.org/authors/?q=ai:wang.rui.29"Wang, Xiaole"https://zbmath.org/authors/?q=ai:wang.xiaole"Xiao, Zuoli"https://zbmath.org/authors/?q=ai:xiao.zuoli"Liu, Feng"https://zbmath.org/authors/?q=ai:liu.feng.1Summary: An adaptive time spectral viscosity (TSV) approach is proposed to stabilize the time-spectral method (TSM) by dealiasing its solution. Instead of being assigned uniformly in space, the cut-off wave number for TSV is determined locally by spectrum analysis of the flow variables. On each grid cell, the significant low-frequency modes are adaptively separated from the TSV targeted high-frequency ones according to local flow physics. The space-time Lower-Upper Symmetric Gauss-Seidel(ST-LU-SGS) implicit scheme is used to solve the modified time-spectral equations. TSV operator is treated implicitly in the same way as the time spectral operator to facilitate fast convergence. Computational results of inviscid and turbulent flows over a pitching NACA0012 airfoil are presented for validation of the adaptive TSV approach. For the turbulent flow case, the proposed approach is also applied to the Spalart-Allmaras (S-A) turbulence model equation. The accuracy and the convergence rate of the adaptive TSV approach is demonstrated in both test cases.The \(\delta \)-ALE-SPH model: an arbitrary Lagrangian-Eulerian framework for the \(\delta \)-SPH model with particle shifting techniquehttps://zbmath.org/1521.766272023-11-13T18:48:18.785376Z"Antuono, M."https://zbmath.org/authors/?q=ai:antuono.matteo"Sun, P. N."https://zbmath.org/authors/?q=ai:sun.pengnan|sun.punan"Marrone, S."https://zbmath.org/authors/?q=ai:marrone.salvatore"Colagrossi, A."https://zbmath.org/authors/?q=ai:colagrossi.andreaSummary: The behaviour of a weakly-compressible SPH scheme obtained by rewriting the Navier-Stokes equations in an arbitrary Lagrangian-Eulerian (ALE) format is studied. Differently from previous works on ALE, which generally adopt conservative variables (i.e. mass and momentum) and rely on the use of Riemann solvers inside the spatial operators, the proposed model is expressed in terms of primitive variables (i.e. density and velocity) and is written by using the standard differential formulations of the weakly-compressible SPH schemes. Similarly to ALE-SPH models, the arbitrary velocity field is obtained by modifying the pure Lagrangian velocity of the material point through a velocity \(\delta \overrightarrow{u}\) given by a Particle Shifting Technique (PST). We show that the above-mentioned ALE-SPH equations are, however, unstable when they are integrated in time. The instability appears in the form of large volume variations in those fluid regions characterised by high velocity strain rates. Nonetheless, the scheme can be stabilised if appropriate diffusion terms are included in both the equations of density and mass. This latter scheme, hereinafter called \(\delta \)-ALE-SPH scheme, is validated against reference benchmark test-cases: the viscous flow around an inclined elliptical cylinder, the lid-driven cavity and a dam-break flow impacting a vertical wall.Moments-based method for boundary conditions in the lattice Boltzmann framework: a comparative analysis for the lid driven cavity flowhttps://zbmath.org/1521.766312023-11-13T18:48:18.785376Z"Bazarin, R. L. M."https://zbmath.org/authors/?q=ai:bazarin.r-l-m"Philippi, P. C."https://zbmath.org/authors/?q=ai:philippi.paulo-cesar"Randles, A."https://zbmath.org/authors/?q=ai:randles.amanda"Hegele, L. A."https://zbmath.org/authors/?q=ai:hegele.luiz-a|hegele.l-a-jrSummary: Dealing with boundary conditions (BC) was ever considered a puzzling question in the lattice Boltzmann (LB) method. The most popular BC models are based on Ad-Hoc rules and, although these BC models were shown to be suitable for low-order LB equations, their extension to high-order LB was shown to be a very difficult problem and, at authors knowledge, never solved with satisfaction. The main question to be solved is how to deal with a problem when the number of unknowns (the particle populations coming from the outside part of the numerical domain) is greater than the number of equations at our disposal at each boundary site. Recently, BC models based on the regularization of the LB equation, or moments-based models, were proposed. These moments replace the discrete populations as unknowns, independently of the number of discrete velocities that are needed for solving a given problem. The full set of moments-based BC leads, nevertheless, to an overdetermined system of equations, and what distinguishes one model from another is the way this system is solved. In contrast with previous work, we base our approach on second-order moments. Four versions of this model are compared with previous moments-based models considering, in addition to the accuracy, some main model attributes such as global and local mass conservation, rates of convergence, and stability. For this purpose, the complex flow patterns displayed in a two-dimensional lid-driven cavity are investigated.Intrusive generalized polynomial chaos with asynchronous time integration for the solution of the unsteady Navier-Stokes equationshttps://zbmath.org/1521.766322023-11-13T18:48:18.785376Z"Bonnaire, P."https://zbmath.org/authors/?q=ai:bonnaire.p"Pettersson, P."https://zbmath.org/authors/?q=ai:pettersson.peter|pettersson.per|pettersson.paul"Silva, C. F."https://zbmath.org/authors/?q=ai:silva.camilo-fSummary: Generalized polynomial chaos provides a reliable framework for many problems of uncertainty quantification in computational fluid dynamics. However, it fails for long-time integration of unsteady problems with stochastic frequency. In this work, the asynchronous time integration technique, introduced in previous works to remedy this issue for systems of ODEs, is applied to the Kármán vortex street problem. For this purpose, we make use of a stochastic clock speed that provides the phase shift between the realizations and enables the simulation of an in-phase behavior. Results of the proposed method are validated against Monte Carlo simulations and show good results for statistic fields and point-wise values such as phase portraits, as well as PDFs of the limit cycle. We demonstrate that low-order expansions are sufficient to meet the demands for some statistic measures. Therefore, computational costs are still competitive with those of the standard form of intrusive generalized polynomial chaos (igPC) and its non-intrusive counterpart (NigPC).Improving stability of moving particle semi-implicit method by source terms based on time-scale correction of particle-level impulseshttps://zbmath.org/1521.766352023-11-13T18:48:18.785376Z"Cheng, Liang-Yee"https://zbmath.org/authors/?q=ai:cheng.liang-yee"Augusto Amaro Junior, Rubens"https://zbmath.org/authors/?q=ai:augusto-amaro.rubens-jun"Henrique Favero, Eric"https://zbmath.org/authors/?q=ai:henrique-favero.ericSummary: The aim of this paper is to investigate the unstable nature of pressure computation focusing on incompressible flow modeling through the projection-based particle methods. A new approach from the original viewpoint of the momentum conservation regarding particle-level collisions, hereinafter refered to as time-scale correction of particle-level impulses (TCPI), is proposed to derive new source terms of pressure Poisson equation (PPE). This results in more stable computations with drastic reduction of unphysical pressure oscillations and more robust simulation with pressure magnitudes almost independent to time step. Moreover, compared to other strategies, no additional computational effort is required, its implementation is extremely simple, and the only numerical parameter is the propagation speed of the perturbations, of which the calibration is much more straightforward due to its physical meaning. Simulations were carried out using moving particle semi-implicit (MPS) method improved by the proposed approach. The comparisons of computed results with theoretical and experimental ones confirmed the effectiveness of the proposed approach.A new SPH density formulation for 3D free-surface flowshttps://zbmath.org/1521.766542023-11-13T18:48:18.785376Z"Geara, S."https://zbmath.org/authors/?q=ai:geara.s"Martin, S."https://zbmath.org/authors/?q=ai:martin.segolene|martin.sebastian|martin.stephen-r|martin.sandra-l|martin.spencer|martin.sergio-m|martin.stefano|martin.stephen-p|martin.samuel|martin.silvio-ulrich|martin.sebastia|martin.stephan|martin.seelye|martin.scott-p|martin.saul|martin.samuel.1|martin.sylvain|martin.susan|martin.santiago-brouard|martin.sean-c|martin.stephen-e|martin.steve|martin.samuel-gil|martin.simon-p|martin.sara-r|martin.sebastien|martin.sophie|martin.shawn|martin.steven-w|martin.sebastien.1"Adami, S."https://zbmath.org/authors/?q=ai:adami.stefania|adami.stefan"Petry, W."https://zbmath.org/authors/?q=ai:petry.walter"Allenou, J."https://zbmath.org/authors/?q=ai:allenou.j"Stepnik, B."https://zbmath.org/authors/?q=ai:stepnik.b"Bonnefoy, O."https://zbmath.org/authors/?q=ai:bonnefoy.olivierSummary: In this paper, a new density formulation for free surface simulations using SPH is presented. This new approach is applicable to surface-tension driven free surface flows with strong topological changes. The density is corrected for each particle by analytically calculating the missing volume of the support domain. This calculation depends on two parameters: the local curvature and the distance of each particle to the free surface. This method was validated and compared with the density evolution method for two test cases: the square droplet and the Rayleigh-Plateau instability. It shows more stable results and a better representation of the free surface.An arbitrary Lagrangian Eulerian smoothed particle hydrodynamics (ALE-SPH) method with a boundary volume fraction formulation for fluid-structure interactionhttps://zbmath.org/1521.766682023-11-13T18:48:18.785376Z"Jacob, Bruno"https://zbmath.org/authors/?q=ai:jacob.bruno"Drawert, Brian"https://zbmath.org/authors/?q=ai:drawert.brian"Yi, Tau-Mu"https://zbmath.org/authors/?q=ai:yi.tau-mu"Petzold, Linda"https://zbmath.org/authors/?q=ai:petzold.linda-ruthSummary: We present a new weakly-compressible smoothed particle hydrodynamics (SPH) method capable of modeling non-slip fixed and moving wall boundary conditions. The formulation combines a boundary volume fraction (BVF) wall approach with the transport-velocity SPH method. The resulting method, named SPH-BVF, offers detection of arbitrarily shaped solid walls on-the-fly, with small computational overhead due to its local formulation. This simple framework is capable of solving problems that are difficult or infeasible for standard SPH, namely flows subject to large shear stresses or at moderate Reynolds numbers, and mass transfer in deformable boundaries. In addition, the method extends the transport-velocity formulation to reaction-diffusion transport of mass in Newtonian fluids and linear elastic solids, which is common in biological structures. Taken together, the SPH-BVF method provides a good balance of simplicity and versatility, while avoiding some of the standard obstacles associated with SPH: particle penetration at the boundaries, tension instabilities and anisotropic particle alignments, that hamper SPH from being applied to complex problems such as fluid-structure interaction in a biological system.An exact non-equilibrium extrapolation scheme for pressure and velocity boundary conditions with large gradients in the lattice Boltzmann methodhttps://zbmath.org/1521.766712023-11-13T18:48:18.785376Z"Ju, Long"https://zbmath.org/authors/?q=ai:ju.long"Shan, Baochao"https://zbmath.org/authors/?q=ai:shan.baochao"Yang, Zhou"https://zbmath.org/authors/?q=ai:yang.zhou"Guo, Zhaoli"https://zbmath.org/authors/?q=ai:guo.zhaoliSummary: In this work, an exact non-equilibrium extrapolation (eNEQ) scheme for velocity and pressure boundary conditions in the lattice Boltzmann method is proposed. Based on the non-equilibrium extrapolation (NEQ) scheme, well designed parameters are introduced to correct the distribution functions. Numerical results of velocity and pressure driven Poiseuille flows demonstrate that the present eNEQ scheme is of second-order spatial accuracy for both velocity and pressure boundary conditions. In addition, a series of other numerical simulation results show that in some cases with the large pressure or velocity gradient at the boundary, the eNEQ scheme can well ensure the accuracy of the calculation results, while the NEQ scheme performs struggle due to the adoption of the extrapolation scheme. On the basis of retaining the advantages of the original NEQ scheme, the present eNEQ scheme can be used to implement the velocity and pressure boundary conditions exactly.Stokes eigenmodes on two-dimensional regular polygonshttps://zbmath.org/1521.766752023-11-13T18:48:18.785376Z"Lallemand, Pierre"https://zbmath.org/authors/?q=ai:lallemand.pierre"Chen, Lizhen"https://zbmath.org/authors/?q=ai:chen.lizhen.1"Labrosse, Gérard"https://zbmath.org/authors/?q=ai:labrosse.gerard"Luo, Li-Shi"https://zbmath.org/authors/?q=ai:luo.lishiSummary: The Stokes eigenmodes on two-dimensional regular polygons of \(N\) apexes, \( 3 \leq N \leq 40\), are studied numerically using two different solvers: the lattice Boltzmann equation and the Legendre-Galerkin spectral element method. In particular, the lowest 55 eigenmodes on regular \(N\)-polygons have been computed and investigated for the following properties including (a) symmetries, (b) the asymptotic behaviour of the Stokes eigenvalues \(\lambda ( N )\) in the limit of the apex number \(N \to \infty \), \textit{i.e.}, in the limit of a regular \(N\)-polygon becoming its circumcircle, (c) the splitting doublet modes due to boundary geometry of \(N\)-polygons, and (d) the one-to-one correspondence between the Stokes modes on regular \(N\)-polygons and on the disc.Diffuse bounce back condition for lattice Boltzmann methodhttps://zbmath.org/1521.766782023-11-13T18:48:18.785376Z"Liu, Geng"https://zbmath.org/authors/?q=ai:liu.geng"Lee, Taehun"https://zbmath.org/authors/?q=ai:lee.taehunSummary: The lattice Boltzmann method has been widely used in curved and moving boundary fluid simulations. Both explicit and implicit treatments are studied to recover proper boundary conditions on Cartesian grids. These methods can describe curved boundaries more accurately and more smoothly than the staircase approximation. However, to improve the order of accuracy and to reduce the fluctuation of force, complicated modifications have been applied to the collision step of lattice Boltzmann equation. In this study, a new boundary scheme based on diffuse geometry is proposed for lattice Boltzmann method. The scheme is derived by directly incorporating the bounce back condition into the weak form of the streaming step of discretized Boltzmann equation. The new method does not change the collision operator. Therefore it can be easily combined with complex collision models. Although diffuse boundary is introduced, this scheme recovers exact bounce back condition at sharp boundary limit, regardless of the shapes and motions of the boundaries. Numerical tests show that the accuracy of this method is second order and depends on the boundary thickness and several other factors. In moving boundary problems, the fluctuation of force can be largely reduced compared to popular sharp boundary conditions because it does not require extrapolation to fulfil the unknown information of the newly generated fluid nodes around the boundaries. In this paper the detailed derivation for the new scheme is explained and the benchmark problems are solved to test its accuracy and the effect of different parameters.Fluids flow in granular aggregate packings reconstructed by high-energy X-ray computed tomography and lattice Boltzmann methodhttps://zbmath.org/1521.766812023-11-13T18:48:18.785376Z"Lyu, Qifeng"https://zbmath.org/authors/?q=ai:lyu.qifeng"Chen, Anguo"https://zbmath.org/authors/?q=ai:chen.anguo"Jia, Jie"https://zbmath.org/authors/?q=ai:jia.jie"Singh, Amardeep"https://zbmath.org/authors/?q=ai:singh.amardeep"Dai, Pengfei"https://zbmath.org/authors/?q=ai:dai.pengfeiSummary: Properties of fluids flow in granular aggregates are important for the design of pervious infrastructures used to alleviate urban water-logging problems. Here in this work, five groups of aggregates packing with similar average porosities but varying particle sizes were scanned by a high-energy X-ray computed tomography (X-CT) facility. The structures of the packings were reconstructed. Porosities were calculated and compared with those measured by the volume and mass of infilled water in the packing. Then pore networks were extracted and analyzed. Simulations of fluids flow in the packings were performed by using a lattice Boltzmann method (LBM) with BGK (Bhatnagar-Gross-Krook) collision model in the pore-network domain of the packings. Results showed wall effect on the porosity of aggregates packing was significant and the influence increased with the aggregate sizes. In addition, Poisson law and power law can be used to fit the coordination number and coordination volume of the packing's pore network, respectively. Moreover, the mass flow rates of fluids in the aggregates were affected by the porosities. On the two-dimensional slices, the mass flow rate decreased when the slice porosity increased. But for the three-dimensional blocks, the average mass flow rate increased with the volume porosity. And the permeability of the aggregates packing showed correlating change trend with the average pore diameter and fitting parameters of coordination volumes, when the sizes of aggregates changed. Though the limitation of merging interfaces causing fluctuation and discontinuity on micro parameters of fluid flow existed, the methods and results here may provide knowledge and insights for numerical simulations and optimal design of aggregate-based materials.A refined moving particle pressure mesh (MPPM) method for solving incompressible Navier-Stokes equationshttps://zbmath.org/1521.766862023-11-13T18:48:18.785376Z"Ng, Y. L."https://zbmath.org/authors/?q=ai:ng.y-l"Ng, K. C."https://zbmath.org/authors/?q=ai:ng.khai-ching"Sheu, T. W. H."https://zbmath.org/authors/?q=ai:sheu.tony-wen-hannSummary: From the previous works, we found that the stability of the pressure solution obtained by using particle-based method can be improved by solving the pressure equation on a stationary Eulerian grid. In this study, the Multiquadric Radial Basis Function (RBF-MQ) interpolation technique is applied for the data transfer between Lagrangian particles and Eulerian grids in solving the incompressible Navier-Stokes equations. Also, the argument on selecting the optimal shape parameter (for MQ kernel) is resolved in the current work as well by using the information of the surrounding nodes. In order to preserve the continuity constraint on the particle level, the divergence-free interpolation scheme is proposed to interpolate the velocity from grid to particle. For validation purpose, a series of flow cases are solved by using the current Moving Particle with Pressure Mesh (MPPM) method and good agreement has been found between the current and the benchmark solutions. Also, we found that the current method is more accurate than our previous MPPM method.A lattice-Boltzmann-based perturbation methodhttps://zbmath.org/1521.766882023-11-13T18:48:18.785376Z"O'Reilly, Christopher M."https://zbmath.org/authors/?q=ai:oreilly.christopher-m"Janßen, Christian F."https://zbmath.org/authors/?q=ai:janssen.christian-f"Grilli, Stephan T."https://zbmath.org/authors/?q=ai:grilli.stephan-tSummary: In this work, we report on the development and initial validation of a new hybrid numerical model for the simulation of incompressible flow. A kinetic Lattice Boltzmann method (LBM) model using a reduced domain is nested within an inviscid flow field to provide increased simulation fidelity where desired, while leveraging the computational efficiency of inviscid solutions. We formulate a fully (or strongly) coupled approach, in which a Helmholtz decomposition is applied to the flow, separating the inviscid and viscous perturbation parts. The latter component is driven by the inviscid field through nonlinear inviscid-perturbation interaction terms that, in conventional Navier-Stokes solvers, would be expressed as volume forces. In the present work an equivalent LBM approach is presented where, as opposed to a body-force coupling, a strong coupling within the LBM collision operators is presented. The resulting hybrid LBM is applied to validation cases for a wave driven boundary layer and the flow past a cylinder.Dual-time smoothed particle hydrodynamics for incompressible fluid simulationhttps://zbmath.org/1521.766922023-11-13T18:48:18.785376Z"Ramachandran, Prabhu"https://zbmath.org/authors/?q=ai:ramachandran.prabhu"Muta, Abhinav"https://zbmath.org/authors/?q=ai:muta.abhinav"Ramakrishna, M."https://zbmath.org/authors/?q=ai:ramakrishna.m-v|ramakrishna.matheSummary: In this paper we propose a dual-time stepping scheme for the Smoothed Particle Hydrodynamics (SPH) method. Dual-time stepping has been used in the context of other numerical methods for the simulation of incompressible fluid flows. Here we provide a scheme that combines the entropically damped artificial compressibility (EDAC) along with dual-time stepping. The method is accurate, robust, and demonstrates up to seven times better performance than the standard weakly-compressible formulation. We demonstrate several benchmarks showing the applicability of the scheme. In addition, we provide a completely open source implementation and a reproducible manuscript.An SPH-based fully-Lagrangian meshfree implicit FSI solver with high-order discretization termshttps://zbmath.org/1521.766972023-11-13T18:48:18.785376Z"Shimizu, Yuma"https://zbmath.org/authors/?q=ai:shimizu.yuma"Khayyer, Abbas"https://zbmath.org/authors/?q=ai:khayyer.abbas"Gotoh, Hitoshi"https://zbmath.org/authors/?q=ai:gotoh.hitoshi(no abstract)A preconditioned lattice Boltzmann flux solver for steady flows on unstructured hexahedral gridshttps://zbmath.org/1521.767072023-11-13T18:48:18.785376Z"Walsh, Brendan"https://zbmath.org/authors/?q=ai:walsh.brendan"Boyle, Fergal J."https://zbmath.org/authors/?q=ai:boyle.fergal-jSummary: The lattice Boltzmann flux solver (LBFS), first introduced by \textit{C. Shu} et al. [``Development of lattice Boltzmann flux solver for simulation of incompressible flows'', Adv. Appl. Math. Mech. 6, No. 4, 436--460 (2014; \url{doi:10.4208/aamm.2014.4.s2})] on structured meshes, allows fluid flow problems to be solved on unstructured meshes discretised by the finite volume method. The solver calculates the macroscopic fluxes at the cell interfaces from a local reconstruction of the lattice Boltzmann solution. In this paper the LBFS is extended to three-dimensional unstructured hexahedral meshes and a preconditioned lattice Boltzmann flux solver (PLBFS) is presented. The PLBFS involves applying the preconditioning technique proposed by \textit{Z. Guo} et al. [``Preconditioned lattice-Boltzmann method for steady flows'', Phys. Rev. E (3) 70, No. 6, Article ID 066706, 8 p. (2004; \url{doi:10.1103/PhysRevE.70.066706})]) to the LBFS and is achieved by modifying the equilibrium distribution function used to calculate the macroscopic fluxes at the cell interface. When the PLBFS is applied to steady flow problems, it is shown that convergence is significantly accelerated and the accuracy of predictions with unstructured grids is greatly improved when compared to the LBFS. This paper also introduces a strategy for choosing the optimal value of preconditioning factor with unstructured hexahedral meshes.Stratified Taylor-Green vortex by lattice Boltzmann methods: influence of stencils, forcing schemes, and collision modelshttps://zbmath.org/1521.767152023-11-13T18:48:18.785376Z"Wilde, Dominik"https://zbmath.org/authors/?q=ai:wilde.dominik"Nidhan, Sheel"https://zbmath.org/authors/?q=ai:nidhan.sheel"Pham, Hieu T."https://zbmath.org/authors/?q=ai:pham.hieu-t"Foysi, Holger"https://zbmath.org/authors/?q=ai:foysi.holger"Reith, Dirk"https://zbmath.org/authors/?q=ai:reith.dirk"Sarkar, Sutanu"https://zbmath.org/authors/?q=ai:sarkar.sutanuSummary: Stably stratified Taylor-Green vortex simulations are performed by lattice Boltzmann methods (LBM) and compared to other recent works using Navier-Stokes solvers. The density variation is modeled with a separate distribution function in addition to the particle distribution function modeling the flow physics. Different stencils, forcing schemes, and collision models are tested and assessed. The overall agreement of the lattice Boltzmann solutions with reference solutions from other works is very good, even when no explicit subgrid model is used, but the quality depends on the LBM setup. Although the LBM forcing scheme is not decisive for the quality of the solution, the choice of the collision model and of the stencil are crucial for adequate solutions in underresolved conditions. The LBM simulations confirm the suppression of vertical flow motion for decreasing initial Froude numbers. To gain further insight into buoyancy effects, energy decay, dissipation rates, and flux coefficients are evaluated using the LBM model for various Froude numbers.Reduction-consistent multiple-relaxation-time lattice Boltzmann equation method for wall bounded \(N\) immiscible incompressible fluidshttps://zbmath.org/1521.767252023-11-13T18:48:18.785376Z"Zheng, Lin"https://zbmath.org/authors/?q=ai:zheng.lin"Zheng, Song"https://zbmath.org/authors/?q=ai:zheng.song"Zhai, Qinglan"https://zbmath.org/authors/?q=ai:zhai.qinglanSummary: A multiple-relaxation-time (MRT) lattice Boltzmann equation (LBE) method is developed for \(N\)-phase \((N\geq 2)\) flow with moving contact lines. In the model, MRT LBE is applied to solve the incompressible Navier-Stokes equation, and another MRT LBE is developed for fluid-fluid interface capturing, where the MRT LBE has the reduction-consistent property and can guarantee the mass conservation of each phase. The wettability of solid in the presence of \(N\) \((N\geq 2)\) immiscible fluids can be achieved by a reduction-consistent wettability boundary condition, which can treat different contact angle between the fluids and the solid. A series of benchmark tests such as spreading of droplets and compound droplet on a solid wall, and compound droplet impact on a dry solid wall are conducted to validate the MRT LBEs, and it is shown that the predictions of LBE agree well with the theory/other numerical results.Deposition pattern of drying dropletshttps://zbmath.org/1521.767272023-11-13T18:48:18.785376Z"Yang, Xiuyuan"https://zbmath.org/authors/?q=ai:yang.xiuyuan"Jiang, Zechao"https://zbmath.org/authors/?q=ai:jiang.zechao"Lyu, Peihan"https://zbmath.org/authors/?q=ai:lyu.peihan"Ding, Zhaoyu"https://zbmath.org/authors/?q=ai:ding.zhaoyu"Man, Xingkun"https://zbmath.org/authors/?q=ai:man.xingkunSummary: The drying of liquid droplets is a common daily life phenomenon that has long held a special interest in scientific research. When the droplet includes nonvolatile solutes, the evaporation of the solvent induces rich deposition patterns of solutes on the substrate. Understanding the formation mechanism of these patterns has important ramifications for technical applications, ranging from coating to inkjet printing to disease detection. This topical review addresses the development of physical understanding of tailoring the specific ring-like deposition patterns of drying droplets. We start with a brief introduction of the experimental techniques that are developed to control these patterns of sessile droplets. We then summarize the development of the corresponding theory. Particular attention herein is focused on advances and issues related to applying the Onsager variational principle (OVP) theory to the study of the deposition patterns of drying droplets. The main obstacle to conventional theory is the requirement of complex numerical solutions, but fortunately there has been recent groundbreaking progress due to the OVP theory. The advantage of the OVP theory is that it can be used as an approximation tool to reduce the high-order conventional hydrodynamic equations to first-order evolution equations, facilitating the analysis of soft matter dynamic problems. As such, OVP theory is now well poised to become a theory of choice for predicting deposition patterns of drying droplets.Cylinder drag minimization through wall actuation: a Bayesian optimization approachhttps://zbmath.org/1521.767312023-11-13T18:48:18.785376Z"Larroque, Anthony"https://zbmath.org/authors/?q=ai:larroque.anthony"Fosas de Pando, Miguel"https://zbmath.org/authors/?q=ai:fosas-de-pando.miguel"Lafuente, Luis"https://zbmath.org/authors/?q=ai:lafuente.luisSummary: Bayesian Optimization (BO) has recently gained popularity as an efficient derivative-free method for the global optimization of expensive noisy black-box objective functions. These characteristics render BO a promising tool to tackle optimization problems involving numerical simulations of complex unsteady flows at moderate-to-high Reynolds numbers. In this work, we assess the efficiency of Bayesian Optimization by considering two canonical flow problems: the drag reduction in the two-dimensional and three-dimensional flow around circular cylinders at, respectively, \(\mathrm{Re} = 500\) and \(\mathrm{Re} = 3900\), through tangential-velocity actuation at the cylinder wall. The root-mean-square of the drag coefficient with and without penalty terms is considered as the objective function. Several variants of Bayesian Optimization are assessed and compared against competing optimization algorithms such as Particle Swarm Optimization, CMA-ES, Nelder-Mead and the Explorative Gradient Method. Results show that in this case, the serial and the parallel BO techniques outperform other algorithms.Fluid dynamics problems in uncertain environmenthttps://zbmath.org/1521.767332023-11-13T18:48:18.785376Z"Karunakar, Perumandla"https://zbmath.org/authors/?q=ai:karunakar.perumandla"Biswal, Uddhaba"https://zbmath.org/authors/?q=ai:biswal.uddhaba"Chakraverty, Snehashish"https://zbmath.org/authors/?q=ai:chakraverty.snehashishSummary: The study of fluid flow in convergent and divergent channels is very important because of their vast application in engineering and industrial field such as heat exchangers for milk flowing, cold drawing operation in polymer industry, etc. The constants related to diffusion power are crisp numbers, but they may not be crisp always because these are measured values. To handle these involved uncertainties, the authors consider them as interval numbers, which transform the governing coupled Whitham-Broer-Kaup equations (CWBK) equations to interval CWBK equations. They discuss some basic concept of interval/fuzzy theory and some notations. The authors also discuss two problems, namely, Jeffery-Hamel problem and CWBK shallow water equations. They illustrate two efficient semianalytical methods, namely, homotopy perturbation method and homotopy perturbation transform method, which are useful in solving fluid-related problems in both crisp and uncertain environments.
For the entire collection see [Zbl 1439.74003].Application of a local meshless modified characteristic method to incompressible fluid flows with heat transport problemhttps://zbmath.org/1521.767582023-11-13T18:48:18.785376Z"Tabbakh, Zineb"https://zbmath.org/authors/?q=ai:tabbakh.zineb"Ellaia, Rachid"https://zbmath.org/authors/?q=ai:ellaia.rachid"Ouazar, Driss"https://zbmath.org/authors/?q=ai:ouazar.drissSummary: Radial basis function (RBF) has been accurately used for the spatial discretization to solve PDE problems. In this paper, a practical stabilization of the local formulation of the radial basis function (RBF) method is presented to solve the incompressible fluid flows with heat transport problems. To avoid the nonlinearity of the convective term, we include the modified method of characteristics to construct stable and efficient methods. The governing equations are the incompressible Navier-Stokes equations/Boussinesq approximation coupled with the heat transport equation. The spatial discretization carried out using the local radial basis function (LRBF) method on a uniform and non-uniform nodes distribution in a complex domain. The proposed method can be described as a fractional step splitting where the convective and generalized Stokes parts are treated separately. To solve the generalized Stokes problem, we used a projection/fractional step method that requires velocity-pressure decoupling. The proposed approach's performance is tested on three benchmark problems and natural convection flow in a regular and irregular domains. We compare the results with different numerical solutions published in the literature. The obtained numerical results demonstrate the accuracy and stability of the proposed meshless method.On small perturbations of thermocapillary stationary two-layer flow in plane layer with movable boundaryhttps://zbmath.org/1521.767842023-11-13T18:48:18.785376Z"Andreev, Viktor K."https://zbmath.org/authors/?q=ai:andreev.viktor-konstantinovich"Bekezhanova, Viktoriya B."https://zbmath.org/authors/?q=ai:bekezhanova.viktoriya-bSummary: Problem on plane unidirectional two-layer flow of viscous heat-conducting fluid in microgravity is studied. There is a situation in which the flow is generated by Marangoni forces and motion of one of channel's walls only. Using the linearization method the stability of the regime is investigated. The flow crisis is induced by thermal oscillatory or monotonic waves for different wavenumber.On the theory of slope flows over a thermally inhomogeneous surfacehttps://zbmath.org/1521.768202023-11-13T18:48:18.785376Z"Ingel', L. Kh."https://zbmath.org/authors/?q=ai:ingel.lev-khannanovich|ingel.lev-khanaanovichSummary: A two-dimensional stationary linear model of flows arising in a stably (neutral) stratified medium over a thermally inhomogeneous flat inclined surface is analyzed analytically. Temperature deviations that harmonically depend on the horizontal coordinate transverse to the slope are set at the lower boundary. Explicit analytical solutions allowing one to analyze emerging density flows are obtained. It is shown that these flows can qualitatively differ, depending on the ratio of the slope angle of the lower boundary and the analog of the Rayleigh number. An expression for the latter includes the horizontal scale of the thermal inhomogeneity region as a spatial scale. An appropriate criterion for distinguishing these flows is established.Analysis of a double layer porous hybrid journal bearing considering the combined influence of wear and non-Newtonian behaviour of lubricanthttps://zbmath.org/1521.768392023-11-13T18:48:18.785376Z"Singh, Anil"https://zbmath.org/authors/?q=ai:singh.anil"Sharma, Satish C."https://zbmath.org/authors/?q=ai:sharma.satish-chandSummary: Use of porous materials in fluid film is well established so as to make more uniform distribution of pressure along the journal surface. The work presented in this paper deals with theoretical examination into the effect of worn bearing surface on the behaviour of a hybrid double layer porous journal bearing system (\(\mathrm{DLPJB_S}\)) operating with power-law lubricants. The governing equation for the flow of non-Newtonian lubricant in the bearing porous clearance space is solved by using the FEM. The effects of non-Newtonian lubricant on the bearing characteristics of a worn bearing have been studied. Findings of this study indicates that the hybrid \(\mathrm{DLPJB_S}\) operating under non-Newtonian lubricant offers enhanced values of \(\bar{h}_{min}\), \(\bar{\omega}_{th}\) and rotor dynamic coefficients (stiffness and damping coefficients).Upscaling unsaturated flows in vertically heterogeneous porous layershttps://zbmath.org/1521.768482023-11-13T18:48:18.785376Z"Zheng, Zhong"https://zbmath.org/authors/?q=ai:zheng.zhongSummary: Characterising interfacial and unsaturated flows in heterogeneous porous layers is of both fundamental and practical interest. Under the assumption of vertical gravitational-capillary equilibrium, we present a theoretical model to describe one-dimensional flows in a porous layer with vertical variations in average pore size, porosity, intrinsic permeability and capillary pressure jump between invading and displaced fluids. The model leads to asymptotic solutions for the saturation distribution and outer envelope of the invading fluid, and for the background pressure drop across the porous layer. Eight dimensionless parameters are recognised after appropriate non-dimensionalisation of the governing equations, the influence of which is demonstrated through a series of example calculations. In particular, four asymptotic regimes are identified, representing unconfined sharp-interface flows, confined sharp-interface flows, unconfined unsaturated flows and confined unsaturated flows. Finally, in the context of flow upscaling, analytical solutions are derived for the effective relative permeability curves on the basis of exact solutions of the saturation field and interface shape, shedding light on the subtle influence of competition between injection/pumping and gravitational forces, wetting and capillary effects, viscosity contrast between the invading and displaced fluids and vertical heterogeneity of the porous layer.Axisymmetric deformation of drops through tubes with symmetric and asymmetric constrictionshttps://zbmath.org/1521.768582023-11-13T18:48:18.785376Z"Kaya, Büşra"https://zbmath.org/authors/?q=ai:kaya.busra"Ceyhan, Umut"https://zbmath.org/authors/?q=ai:ceyhan.umutSummary: Drop deformation in constricted passages plays a vital role in porous media, microfluidic devices, lab-on-a-chip applications, etc. Depending on the viscosity ratio, Capillary number, drop volume and geometry of the constriction, drops may break-up by the snap-off mechanism. Different from the previous studies that consider symmetric single/periodic constrictions, we model a tube with a three-dimensional asymmetric constriction which is natural in porous media or can be used in microfluidic devices for the control of deformation and/or break-up mechanism. We model the motion of drops in Stokes regime and integrate the drop evolution using the axisymmetric boundary integral equations. Compared with the symmetric constrictions, the asymmetry of the constriction affects the snap-off time and thus the volume of the generated daughter droplet after snap-off. The volume is particularly affected by the smoothness of the upstream rather than the downstream of the constriction: more drop volume moves into to the constriction before the snap-off occurs. We show that in the case of a drop does not snap-off while passing through a particular constriction, an asymmetric design of this passage promotes snap-off. Pressure drop variation with time across the tube distinguishes the stages of snap-off from escape. Contrary to the use of two-dimensional models for flows in large aspect ratio microfluidic channels, we finally show that, because of the lack of out-of-plane curvature, planar models of tubular flows may be insufficient to observe certain physics such as jet formation and snap-off.Existence and uniqueness for a convective phase change model with temperature-dependent viscosityhttps://zbmath.org/1521.768852023-11-13T18:48:18.785376Z"Belhamadia, Y."https://zbmath.org/authors/?q=ai:belhamadia.youssef"Deteix, J."https://zbmath.org/authors/?q=ai:deteix.jean"Jaffal-Mourtada, B."https://zbmath.org/authors/?q=ai:jaffal-mourtada.basma"Yakoubi, D."https://zbmath.org/authors/?q=ai:yakoubi.drissSummary: In this article, we consider a class of phase change model with temperature-dependent viscosity, convection and mixed boundary conditions on a bounded domain that reflect melting and solidification in a variety of real-world applications, such as metal casting and crystal growth. The mathematical model, which is based on the enthalpy formulation, takes into consideration the thermophysical differences between the liquid and solid states. The moving liquid-solid interface is explicitly fulfilled as the energy and momentum equations are solved over the full physical domain. Under particular assumptions, we derive various a priori estimates and prove well-posedness results. Numerical simulation of the model employed in the paper is presented as an illustration of an example of a melting problem.Magnetohydrodynamic flow and heat transfer of a hybrid nanofluid over a rotating disk by considering Arrhenius energyhttps://zbmath.org/1521.769132023-11-13T18:48:18.785376Z"Reddy, M. Gnaneswara"https://zbmath.org/authors/?q=ai:reddy.m-gnaneswara"R, Naveen Kumar"https://zbmath.org/authors/?q=ai:r.naveen-kumar"Prasannakumara, B. C."https://zbmath.org/authors/?q=ai:prasannakumara.ballajja-chandrappa"Rudraswamy, N. G."https://zbmath.org/authors/?q=ai:rudraswamy.n-g"Ganesh Kumar, K."https://zbmath.org/authors/?q=ai:kumar.k-ganeshSummary: This research work explores the effect of hybrid nanoparticles on the flow over a rotating disk by using an activation energy model. Here, we considered molybdenum disulfide and ferro sulfate as nanoparticles suspended in base fluid water. The magnetic field is pragmatic normal to the hybrid nanofluid flow direction. The derived nonlinear ordinary differential equations are non-dimensionalized and worked out numerically with the help of Maple software by the RKF-45 method. The scientific results for a non-dimensionalized equation are presented for both nanoparticle and hybrid nanoparticle case. Accoutrements of various predominant restrictions on flow and thermal fields are scanned. Computation estimation for friction factor, local Nusselt number and Sherwood number are also executed. Results reveal that the reduction of the heat transfer rate is greater in hybrid nanoparticles when compared to nanoparticles for increasing values of Eckert Number and the thermal field enhances for the enhanced values of volume fraction.Unconditional finite amplitude stability of a fluid in a mechanically isolated vessel with spatially non-uniform wall temperaturehttps://zbmath.org/1521.769252023-11-13T18:48:18.785376Z"Dostalík, M."https://zbmath.org/authors/?q=ai:dostalik.mark"Průša, V."https://zbmath.org/authors/?q=ai:prusa.vit"Rajagopal, K. R."https://zbmath.org/authors/?q=ai:rajagopal.kumbakonam-ramamaniSummary: A fluid occupying a mechanically isolated vessel with walls kept at spatially non-uniform temperature is in the long run expected to reach the spatially inhomogeneous steady state. Irrespective of the initial conditions the velocity field is expected to vanish, and the temperature field is expected to be fully determined by the steady heat equation. This simple observation is however difficult to prove using the corresponding governing equations. The main difficulties are the presence of the dissipative heating term in the evolution equation for temperature and the lack of control on the heat fluxes through the boundary. Using thermodynamical-based arguments, it is shown that these difficulties in the proof can be overcome, and it is proved that the velocity and temperature perturbations to the steady state actually vanish as the time goes to infinity.Relativistic liquids: GENERIC or EIT?https://zbmath.org/1521.830042023-11-13T18:48:18.785376Z"Gavassino, L."https://zbmath.org/authors/?q=ai:gavassino.lorenzo"Antonelli, M."https://zbmath.org/authors/?q=ai:antonelli.melissa|antonelli.michela|antonelli.miranda-j|antonelli.mattia|antonelli.michele|antonelli.massimo|antonelli.marcoSummary: We study the GENERIC hydrodynamic theory for relativistic liquids formulated by Öttinger and collaborators. We use the maximum entropy principle to derive its conditions for linear stability (in an arbitrary reference frame) and for relativistic causality. In addition, we show that, in the linear regime, its field equations can be recast into a symmetric-hyperbolic form. Once rewritten in this way, the linearised field equations turn out to be a particular realisation of the Israel-Stewart theory, where some of the Israel-Stewart free parameters are constrained. This also allows us to reinterpret the GENERIC framework in view of the principles of extended irreversible thermodynamics and to discuss its physical relevance to model (possibly viscoelastic) fluids.Wind instability of gravitation waves on liquid surface in finite poolhttps://zbmath.org/1521.830252023-11-13T18:48:18.785376Z"Gestrin, S. G."https://zbmath.org/authors/?q=ai:gestrin.s-g"Staravoytova, E. V."https://zbmath.org/authors/?q=ai:staravoytova.e-v(no abstract)Late-time post-merger modeling of a compact binary: effects of relativity, r-process heating, and treatment of transporthttps://zbmath.org/1521.831152023-11-13T18:48:18.785376Z"Haddadi, Milad"https://zbmath.org/authors/?q=ai:haddadi.milad"Duez, Matthew D."https://zbmath.org/authors/?q=ai:duez.matthew-d"Foucart, Francois"https://zbmath.org/authors/?q=ai:foucart.francois"Ramirez, Teresita"https://zbmath.org/authors/?q=ai:ramirez.teresita"Fernández, Rodrigo"https://zbmath.org/authors/?q=ai:fernandez.rodrigo-nobre"Knight, Alexander L."https://zbmath.org/authors/?q=ai:knight.alexander-l"Jesse, Jerred"https://zbmath.org/authors/?q=ai:jesse.jerred"Hébert, Francois"https://zbmath.org/authors/?q=ai:hebert.francois"Kidder, Lawrence E."https://zbmath.org/authors/?q=ai:kidder.lawrence-e"Pfeiffer, Harald P."https://zbmath.org/authors/?q=ai:pfeiffer.harald-p"Scheel, Mark A."https://zbmath.org/authors/?q=ai:scheel.mark-aSummary: Detectable electromagnetic counterparts to gravitational waves from compact binary mergers can be produced by outflows from the black hole-accretion disk remnant during the first 10 s after the merger. Two-dimensional axisymmetric simulations with effective viscosity remain an efficient and informative way to model this late-time post-merger evolution. In addition to the inherent approximations of axisymmetry and modeling turbulent angular momentum transport by a viscosity, previous simulations often make other simplifications related to the treatment of the equation of state and turbulent transport effects. In this paper, we test the effect of these modeling choices. By evolving with the same viscosity the exact post-merger initial configuration previously evolved in Newtonian viscous hydrodynamics, we find that the Newtonian treatment provides a good estimate of the disk ejecta mass but underestimates the outflow velocity. We find that the inclusion of heavy nuclei causes a notable increase in ejecta mass. An approximate inclusion of r-process effects has a comparatively smaller effect, except for its designed effect on the composition.
Diffusion of composition and entropy, modeling turbulent transport effects, has the overall effect of reducing ejecta mass and giving it a speed with lower average and more tightly-peaked distribution. Also, we find significant acceleration of outflow even at distances beyond 10 000 km, so that thermal wind velocities only asymptote beyond this radius and at higher values than often reported.Unified inflation with dark energy in the Nojiri-Odintsov holographic modelhttps://zbmath.org/1521.831722023-11-13T18:48:18.785376Z"Bogdanova, Yu. V."https://zbmath.org/authors/?q=ai:bogdanova.yu-v"Timoshkin, A. V."https://zbmath.org/authors/?q=ai:timoshkin.alexander-vSummary: The unification of the early and late-time universe on the basis of the holographic principle taking into account the properties of the viscosity of the fluid in the spatial Friedman-Lemeter-Robertson-Walker metric is considered. In the description, the idea of generalized holographic dark energy cut-off proposed by Nojiri and Odintsov is used. To study the evolution of the unified Universe, a generalized equation of state of the dark fluid is used, including two asymptotic cases. As an example, a cosmological model with a constant thermodynamic parameter and a constant bulk viscosity is studied. Analytical expression for infrared radius in terms of the particle horizon and the energy conservation law are obtained from the holographic point of view. The viscous fluid describing the unification of the early and late-time Universe is represented as a generalized holographic energy.Far-from-equilibrium attractors with a realistic non-conformal equation of statehttps://zbmath.org/1521.832022023-11-13T18:48:18.785376Z"Alqahtani, Mubarak"https://zbmath.org/authors/?q=ai:alqahtani.mubarakSummary: Using anisotropic hydrodynamics, we examine the existence of early-time attractors of non-conformal systems undergoing Bjorken expansion. In the case of a constant mass, we find that the evolution of the scaled longitudinal pressure is insensitive to variations of initial conditions converging onto an early-time universal curve and eventually merging with the late-time Navier-Stokes attractor (the hydrodynamic attractor). On the other hand, the bulk and the shear viscous corrections do not show an early-time attractor behavior. These results are consistent with previous studies considering a constant mass. When a realistic equation of state is included in the dynamics with a thermal mass, we demonstrate for the first time the absence of strict late-time universal attractors. However, a semi-universal feature of the evolution at very late times remains.Cosmology with viscous generalized Chaplygin gas in \(f(Q)\) gravityhttps://zbmath.org/1521.832082023-11-13T18:48:18.785376Z"Gadbail, Gaurav N."https://zbmath.org/authors/?q=ai:gadbail.gaurav-n"Arora, Simran"https://zbmath.org/authors/?q=ai:arora.simran"Sahoo, P. K."https://zbmath.org/authors/?q=ai:sahoo.pradyumn-kumarSummary: We use the hybrid model of bulk viscosity and generalized chaplygin gas (GCG), named the viscous generalized chaplygin gas (VGCG) model, which is thought to be an alternate dark fluid of the universe. We explore the dynamics of the VGCG model in the framework of the non-metricity \(f(Q)\) gravity using the functional form \(f(Q)=\beta Q^n\), where \(\beta\) and \(n\) are arbitrary constants. For the purpose of constraining model parameters, we use recent observational datasets such as Observational Hubble data, Baryon Acoustic Oscillations, and Type \(I a\) supernovae data. According to our study, the evolution of the deceleration parameter \(q\) and the equation of state (EoS) parameter \(w\) shows a transition from deceleration to an acceleration phase and its deviation from the \(\Lambda\) CDM model.Reflection of an internal wave at an interface representing a rapid increase in viscosityhttps://zbmath.org/1521.860242023-11-13T18:48:18.785376Z"Mchugh, John"https://zbmath.org/authors/?q=ai:mchugh.john-revere|mchugh.john-philip"Grimshaw, Roger"https://zbmath.org/authors/?q=ai:grimshaw.roger-h-jSummary: Internal waves at high altitudes are greatly damped by the drastic increase in molecular viscosity and thermal diffusivity, resulting in important heating and other effects at those altitudes. Here we consider the case where this increase in viscosity is very rapid, idealized as an interface with inviscid flow in the lower layer and constant viscosity in the upper layer. The results show that waves are partially reflected by this interface, with a reflection coefficient that increases monotonically with an increase in the viscosity of the upper layer. This mechanism would have a significant impact on the vertical distribution of thermal energy at high altitudes.Efficient sensing of von Kármán vortices using compressive sensinghttps://zbmath.org/1521.940102023-11-13T18:48:18.785376Z"Bayındır, Cihan"https://zbmath.org/authors/?q=ai:bayindir.cihan"Namlı, Barış"https://zbmath.org/authors/?q=ai:namli.barisSummary: In this paper, we discuss the usage and implementation of the compressive sensing (CS) for the efficient measurement and analysis of the von Kármán vortices. We consider two different flow fields, the flow fields around a circle and an ellipse. We solve the governing \(k - \epsilon\) transport equations numerically in order to model the flow fields around these bodies. Using the time series of the drag, \( C_D ,\) and the lift, \( C_L ,\) coefficients, and their Fourier spectra, we show that compressive sampling can be effectively used to measure and analyze Von Kármán vortices. We discuss the effects of the number of samples on reconstruction and the benefits of using compressive sampling over the classical Shannon sampling in the flow measurement and analysis where Von Kármán vortices are present. We comment on our findings and indicate their possible usage areas and extensions. Our results can find many important applications including but are not limited to measure, control, and analyze vibrations around coastal and offshore structures, bridges, aerodynamics, and Bose-Einstein condensation, just to name a few.