Recent zbMATH articles in MSC 76https://zbmath.org/atom/cc/762022-09-13T20:28:31.338867ZWerkzeugApproximation methods in science and engineeringhttps://zbmath.org/1491.000032022-09-13T20:28:31.338867Z"Jazar, Reza N."https://zbmath.org/authors/?q=ai:jazar.reza-nPublisher's description: \textit{Approximation Methods in Engineering and Science} covers fundamental and advanced topics in three areas: Dimensional Analysis, Continued Fractions, and Stability Analysis of the Mathieu Differential Equation. Throughout the book, a strong emphasis is given to concepts and methods used in everyday calculations. Dimensional analysis is a crucial need for every engineer and scientist to be able to do experiments on scaled models and use the results in real world applications. Knowing that most nonlinear equations have no analytic solution, the power series solution is assumed to be the first approach to derive an approximate solution. However, this book will show the advantages of continued fractions and provides a systematic method to develop better approximate solutions in continued fractions. It also shows the importance of determining stability chart of the Mathieu equation and reviews and compares several approximate methods for that. The book provides the energy-rate method to study the stability of parametric differential equations that generates much better approximate solutions.
\begin{itemize}
\item
Covers practical model-prototype analysis and nondimensionalization of differential equations;
\item
Coverage includes approximate methods of responses of nonlinear differential equations;
\item
Discusses how to apply approximation methods to analysis, design, optimization, and control problems;
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Discusses how to implement approximation methods to new aspects of engineering and physics including nonlinear vibration and vehicle dynamics.
\end{itemize}Book review of: R. J. Hosking and R. L. Dewar, Fundamental fluid mechanics and magnetohydrodynamicshttps://zbmath.org/1491.000252022-09-13T20:28:31.338867Z"Roberts, A. J."https://zbmath.org/authors/?q=ai:roberts.andrew-j|roberts.anthony-johnReview of [Zbl 1332.76001].Book review of: M. Asadzadeh, An introduction to the finite element method for differential equationshttps://zbmath.org/1491.000262022-09-13T20:28:31.338867Z"Sachs, Ekkehard"https://zbmath.org/authors/?q=ai:sachs.ekkehard-wReview of [Zbl 1446.65001].Partial differentials with applications to thermodynamics and compressible flowhttps://zbmath.org/1491.350012022-09-13T20:28:31.338867Z"Braga da Costa Campos, Luis Manuel"https://zbmath.org/authors/?q=ai:braga-da-costa-campos.luis-manuel"Vilela, Luís António Raio"https://zbmath.org/authors/?q=ai:vilela.luis-antonio-raioPublisher's description: This book is part of the series ``Mathematics and Physics Applied to Science and Technology.'' It combines rigorous mathematics with general physical principles to model practical engineering systems with a detailed derivation and interpretation of results. The book presents the mathematical theory of partial differential equations and methods of solution satisfying initial and boundary conditions. It includes applications to acoustic, elastic, water, electromagnetic and other waves, to the diffusion of heat, mass and electricity, and to their interactions. The author covers simultaneously rigorous mathematics, general physical principles and engineering applications with practical interest. The book provides interpretation of results with the help of illustrations throughout and discusses similar phenomena, such as the diffusion of heat, electricity and mass. The book is intended for graduate students and engineers working with mathematical models and can be applied to problems in mechanical, aerospace, electrical and other branches of engineering.Homogenization of a coupled incompressible Stokes-Cahn-Hilliard system modeling binary fluid mixture in a porous mediumhttps://zbmath.org/1491.350202022-09-13T20:28:31.338867Z"Lakhmara, Nitu"https://zbmath.org/authors/?q=ai:lakhmara.nitu"Mahato, Hari Shankar"https://zbmath.org/authors/?q=ai:mahato.hari-shankarSummary: A phase-field model for two-phase immiscible, incompressible porous media flow with surface tension effects is considered. The pore-scale model consists of a strongly coupled system of Stokes-Cahn-Hilliard equations. The fluids are separated by an evolving diffuse interface of a finite width depending on the scale parameter \(\varepsilon\) in the considered model. At first, the existence of solution of a coupled system of partial differential equations at micro scale is investigated. We obtained the homogenized equations for the microscopic model via unfolding operator and two-scale convergence approach.Bifurcation structure and stability of steady gravity water waves with constant vorticityhttps://zbmath.org/1491.350232022-09-13T20:28:31.338867Z"Dai, Guowei"https://zbmath.org/authors/?q=ai:dai.guowei"Li, Fengquan"https://zbmath.org/authors/?q=ai:li.fengquan"Zhang, Yong"https://zbmath.org/authors/?q=ai:zhang.yong.10|zhang.yong.12|zhang.yong.13|zhang.yong.9|zhang.yong.15|zhang.yong.2|zhang.yong.1|zhang.yong.11|zhang.yong.8|zhang.yong|zhang.yong.14|zhang.yong.4|zhang.yong.5|zhang.yong.7Summary: This paper studies the local bifurcation direction, stability properties and global structure for a nonlinear pseudodifferential equation, which describes the periodic travelling gravity waves at the free surface of water in a flow of constant vorticity over a flat bed. We first obtain the precise formula of the second derivative of bifurcation parameters at the bifurcation points. In particular, their signs can be strictly judged when constant vorticity vanishes. Furthermore, we present the stability analysis for the travelling water waves that have small vorticity and amplitude. We also show that the global bifurcation curves can't form a loop. Moreover, if the total head is bounded, the existence of waves of all amplitudes from zero up to that of Stokes' highest wave has been established.Asymptotic behavior of solution of Whitham-Broer-Kaup type equations with negative dispersionhttps://zbmath.org/1491.350302022-09-13T20:28:31.338867Z"Bedjaoui, Nabil"https://zbmath.org/authors/?q=ai:bedjaoui.nabil"Kumar, Rajesh"https://zbmath.org/authors/?q=ai:kumar.rajesh-s"Mammeri, Youcef"https://zbmath.org/authors/?q=ai:mammeri.youcefSummary: In this work, we discuss the long time behavior of solutions of the Whitham-Broer-Kaup system with Lipschitz nonlinearity and negative dispersion term. We prove the global well-posedness when \(\alpha+\beta^2<0\) as well as the convergence to 0 of small solutions at rate \(\mathcal{O}(t^{-1/2})\).Improved regularity criteria for the MHD equations in terms of pressure using an Orlicz normhttps://zbmath.org/1491.350952022-09-13T20:28:31.338867Z"Choe, Hi Jun"https://zbmath.org/authors/?q=ai:choe.hi-jun"Neustupa, Jiří"https://zbmath.org/authors/?q=ai:neustupa.jiri"Yang, Minsuk"https://zbmath.org/authors/?q=ai:yang.minsukSummary: We present new regularity criteria in terms of the negative part of the pressure \(p\) or the positive part of the extended Bernoulli pressure \(\mathcal{B} := p + \frac{ 1}{ 2} | \mathbf{u} |^2 + \frac{ 1}{ 2} | \mathbf{b} |^2\), where \(\mathbf{u}\) is the velocity, and \(\mathbf{b}\) is the magnetic field. The criteria extend the previously known results, and the extension is enabled by the use of an appropriate Orlicz norm.On the wave interactions for the drift-flux equations with the Chaplygin gashttps://zbmath.org/1491.352892022-09-13T20:28:31.338867Z"Li, Shuangrong"https://zbmath.org/authors/?q=ai:li.shuangrong"Shen, Chun"https://zbmath.org/authors/?q=ai:shen.chunThe authors study solutions to the system (modeling two-phase flows)
\[
\left\{ \begin{array}{l} \partial_t\rho_1 +\partial_x(\rho_1 u)=0,\\
\partial_t\rho_2 +\partial_x(\rho_2 u)=0,\\
\partial_t\big((\rho_1+\rho_2) u\big) +\partial_x\Big((\rho_1+\rho_2)u^2- (\frac{1}{\rho_1}+\frac{1}{\rho_2})\Big)=0, \end{array}\right.
\]
emerging from piecewise-constant inital data. The system is strictly hyperbolic with all three characteristic fields being linearly degenerate.
The first part of the work deals with the Riemann problem. The authors exhibit two distinct situations: in one case the solution is described through three contact discontinuities, while the other case produces a less standard ``delta shock wave'' solution.
In the second part, the authors investigate the interactions between contact discontinuities and delta shock waves, contact discontinuities and contact discontinuities, delta shock waves and delta shock waves, emerging from piecewise constant initial data with three states.
Reviewer: Vincent Duchêne (Rennes)The Riemann problem for the nonisentropic Baer-Nunziato model of two-phase flowshttps://zbmath.org/1491.352902022-09-13T20:28:31.338867Z"Thanh, Mai Duc"https://zbmath.org/authors/?q=ai:mai-duc-thanh."Vinh, Duong Xuan"https://zbmath.org/authors/?q=ai:vinh.duong-xuanSummary: The Riemann problem for the well-known Baer-Nunziato model of two-phase flows is solved. The system consists of seven partial differential equations with nonconservative terms. The most challenging problem is that this model possesses a double eigenvalue. Although characteristic speeds coincide, the curves of composite waves associated with different characteristic fields can be still constructed. They will also be incorporated into composite wave curves to form solutions of the Riemann problem. Solutions of the Riemann problem will be constructed when initial data are in supersonic regions, subsonic regions, or in both kinds of regions. A unique solution and solutions with resonance are also obtained.Regularization estimates and hydrodynamical limit for the Landau equationhttps://zbmath.org/1491.353102022-09-13T20:28:31.338867Z"Carrapatoso, Kleber"https://zbmath.org/authors/?q=ai:carrapatoso.kleber"Rachid, Mohamad"https://zbmath.org/authors/?q=ai:rachid.mohamad"Tristani, Isabelle"https://zbmath.org/authors/?q=ai:tristani.isabelleSummary: In this paper, we study the Landau equation under the Navier-Stokes scaling in the torus for hard and moderately soft potentials. More precisely, we investigate the Cauchy theory in a perturbative framework and establish some new short time regularization estimates for our rescaled nonlinear Landau equation. These estimates are quantified in time and we obtain the instantaneous expected anisotropic gain of regularity (see [\textit{M. Rachid}, ``Hypoelliptic and spectral estimates for the linearized Landau operator'', Preprint, \url{arXiv:2004.09300}] for the corresponding hypoelliptic estimates on the linearized Landau collision operator). Moreover, the estimates giving the gain of regularity in the velocity variable are uniform in the Knudsen number. Intertwining these new estimates on the Landau equation with estimates on the Navier-Stokes-Fourier system, we are then able to obtain a result of strong convergence towards this fluid system.A stability result for the identification of a permeability parameter on Navier-Stokes equationshttps://zbmath.org/1491.353112022-09-13T20:28:31.338867Z"Aguayo, Jorge"https://zbmath.org/authors/?q=ai:aguayo.jorge"Osses, Axel"https://zbmath.org/authors/?q=ai:osses.axelSecondary flows from a linear array of vortices perturbed principally by a Fourier modehttps://zbmath.org/1491.353122022-09-13T20:28:31.338867Z"Chen, Zhi-Min"https://zbmath.org/authors/?q=ai:chen.zhiminSummary: In the understanding of primary bifurcating flows of a linear array of electromagnetically forced vortices in an experimental fluid motion, a theoretical study on the nonlinear instability is presented. The existence of the bifurcating flows is obtained from a Fourier mode perturbation. This large-scale perturbation, leading to the primary bifurcation observed in a laboratory experiment, was found to be generated principally from a single vortex mode.An exact solution for the semi-stationary compressible Stokes problemhttps://zbmath.org/1491.353132022-09-13T20:28:31.338867Z"Dong, Jianwei"https://zbmath.org/authors/?q=ai:dong.jianweiSummary: In this note, we present an exact solution for the semi-stationary compressible Stokes problem in \(\mathbb{R}^N\). In the case of radial symmetry, an exact solution with velocity of the form \(c(t)r^s\) is obtained for \(s=\frac{1-N\gamma +\gamma}{\gamma +1}\), where \(\gamma >1\) is the adiabatic index and \(r=|x|\). Some interesting properties of the exact solution are analyzed.Low Mach number limit for the full compressible magnetohydrodynamic equations without thermal conductivityhttps://zbmath.org/1491.353142022-09-13T20:28:31.338867Z"Guo, Liang"https://zbmath.org/authors/?q=ai:guo.liang"Li, Fucai"https://zbmath.org/authors/?q=ai:li.fucaiSummary: In this paper we consider the low Mach number limit of the full compressible magnetohydrodynamic equations for the polytropic ideal gas with zero thermal conductivity coefficient in the whole space \(\mathbb{R}^n\) (\(n=2, 3\)). We focus on the case that the pressure varies near its equilibrium state. It means that the density and the temperature may change around their limit functions, and hence generalize the case on the perturbation of the constant states for the density and the temperature. We establish this limit process rigorously when the initial data is well-prepared. Moreover, we also obtain the convergence rates.Stability and periodicity of solutions to Navier-Stokes equations on non-compact Riemannian manifolds with negative curvaturehttps://zbmath.org/1491.353162022-09-13T20:28:31.338867Z"Nguyen, Thieu Huy"https://zbmath.org/authors/?q=ai:nguyen-thieu-huy."Vu, Thi Ngoc Ha"https://zbmath.org/authors/?q=ai:vu-thi-ngoc-ha."Nguyen, Thi Van"https://zbmath.org/authors/?q=ai:van-nguyen.thiSummary: Let \((M, g)\) be a non-compact Riemannian manifold having negative Ricci curvature tensor. Then, we consider the Navier-Stokes Equations (NSE) for vector fields on \((M, g)\) and prove the existence of a bounded solution to NSE on \((M, g)\). Moreover we show the stability on a small neighborhood for such a solution. Then, using such a local stability we show the existence of a time-periodic solution to NSE under the action of a time-periodic external force. Our result can be considered as a Serrin-type theorem for the case of non-compact Riemannian manifolds with negative curvature tensors.Global hydrostatic approximation of the hyperbolic Navier-Stokes system with small Gevrey class 2 datahttps://zbmath.org/1491.353172022-09-13T20:28:31.338867Z"Paicu, Marius"https://zbmath.org/authors/?q=ai:paicu.marius"Zhang, Ping"https://zbmath.org/authors/?q=ai:zhang.ping.3Summary: We investigate the hydrostatic approximation of a hyperbolic version of Navier-Stokes equations, which is obtained by using the Cattaneo type law instead of the Fourier law, evolving in a thin strip \(\mathbb{R} \times (0, \epsilon)\). The formal limit of these equations is a hyperbolic Prandtl type equation. We first prove the global existence of solutions to these equations under a uniform smallness assumption on the data in the Gevrey class 2. Then we justify the limit globally-in-time from the anisotropic hyperbolic Navier-Stokes system to the hyperbolic Prandtl system with such Gevrey class 2 data. Compared with [\textit{M. Paicu} et al., Adv. Math. 372, Article ID 107293, 41 p. (2020; Zbl 1446.35105)] for the hydrostatic approximation of the 2-D classical Navier-Stokes system with analytic data, here the initial data belongs to the Gevrey class 2, which is very sophisticated even for the well-posedness of the classical Prandtl system (see [\textit{H. Dietert} and \textit{D. Gérard-Varet}, Ann. PDE 5, No. 1, Paper No. 8, 51 p. (2019; Zbl 1428.35355)] and [\textit{C. Wang}, \textit{Y. Wang,} and \textit{P. Zhang}, ``On the global small solution of 2-D Prandtl system with initial data in the optimal Gevrey class'', Preprint, \url{arXiv:2103.00681}]); furthermore, the estimate of the pressure term in the hyperbolic Prandtl system give rise to additional difficulties.Existence and uniqueness result for a fluid-structure-interaction evolution problem in an unbounded 2D channelhttps://zbmath.org/1491.353182022-09-13T20:28:31.338867Z"Patriarca, Clara"https://zbmath.org/authors/?q=ai:patriarca.claraSummary: In an unbounded 2D channel, we consider the vertical displacement of a rectangular obstacle in a regime of small flux for the incoming flow field, modelling the interaction between the cross-section of the deck of a suspension bridge and the wind. We prove an existence and uniqueness result for a fluid-structure-interaction evolution problem set in this channel, where at infinity the velocity field of the fluid has a \textit{Poiseuille flow} profile. We introduce a suitable definition of weak solutions and we make use of a penalty method. In order to prevent the obstacle from going excessively far from the equilibrium position and colliding with the boundary of the channel, we introduce a \textit{strong force} in the differential equation governing the motion of the rigid body and we find a unique global-in-time solution.On numerical approximations to fluid-structure interactions involving compressible fluidshttps://zbmath.org/1491.353192022-09-13T20:28:31.338867Z"Schwarzacher, Sebastian"https://zbmath.org/authors/?q=ai:schwarzacher.sebastian"She, Bangwei"https://zbmath.org/authors/?q=ai:she.bangweiSummary: In this paper we introduce a numerical scheme for fluid-structure interaction problems in two or three space dimensions. A flexible elastic plate is interacting with a viscous, compressible barotropic fluid. Hence the physical domain of definition (the domain of Eulerian coordinates) is changing in time. We introduce a fully discrete scheme that is stable, satisfies geometric conservation, mass conservation and the positivity of the density. We also prove that the scheme is consistent with the definition of continuous weak solutions.New thought on Matsumura-Nishida theory in the \(L_p\)-\(L_q\) Maximal regularity frameworkhttps://zbmath.org/1491.353202022-09-13T20:28:31.338867Z"Shibata, Yoshihiro"https://zbmath.org/authors/?q=ai:shibata.yoshihiroSummary: This paper is devoted to proving the global well-posedness of initial-boundary value problem for Navier-Stokes equations describing the motion of viscous, compressible, barotropic fluid flows in a three dimensional exterior domain with non-slip boundary conditions. This was first proved by an excellent paper due to \textit{A. Matsumura} and \textit{T. Nishida} [Commun. Math. Phys. 89, 445--464 (1983; Zbl 0543.76099)]. In [loc. cit.], they used energy method and their requirement was that space derivatives of the mass density up to third order and space derivatives of the velocity fields up to fourth order belong to \(L_2\) in space-time, detailed statement of Matsumura and Nishida theorem is given in Theorem 1 of Sect. 1 of context. This requirement is essentially used to estimate the \(L_\infty\) norm of necessary order of derivatives in order to enclose the iteration scheme with the help of Sobolev inequalities and also to treat the material derivatives of the mass density. On the other hand, this paper gives the global wellposedness of the same problem as in [loc. cit.] in \(L_p\) (\(1 <p \le 2\)) in time and \(L_2\cap L_6\) in space maximal regularity class, which is an improvement of the Matsumura and Nishida theory in [loc. cit.] from the point of view of the minimal requirement of the regularity of solutions. In fact, after changing the material derivatives to time derivatives by Lagrange transformation, enough estimates obtained by combination of the maximal \(L_p\) (\(1 <p \le 2\)) in time and \(L_2\cap L_6\) in space regularity and \(L_p\)-\(L_q\) decay estimate of the Stokes equations with non-slip conditions in the compressible viscous fluid flow case enable us to use the standard Banach's fixed point argument. Moreover, one of the purposes of this paper is to present a framework to prove the \(L_p\)-\(L_q\) maximal regularity for parabolic-hyperbolic type equations with non-homogeneous boundary conditions and how to combine the maximal \(L_p\)-\(L_q\) regularity and \(L_p\)-\(L_q\) decay estimates of linearized equations to prove the global well-posedness of quasilinear problems in unbounded domains, which gives a new thought of proving the global well-posedness of initial-boundary value problems for systems of parabolic or parabolic-hyperbolic equations appearing in mathematical physics.Inviscid limit of the inhomogeneous incompressible Navier-Stokes equations under the weak Kolmogorov hypothesis in \(\mathbb{R}^3\)https://zbmath.org/1491.353222022-09-13T20:28:31.338867Z"Wang, Dixi"https://zbmath.org/authors/?q=ai:wang.dixi"Yu, Cheng"https://zbmath.org/authors/?q=ai:yu.cheng"Zhao, Xinhua"https://zbmath.org/authors/?q=ai:zhao.xinhuaSummary: In this paper, we consider the inviscid limit of inhomogeneous incompressible Navier-Stokes equations under the weak Kolmogorov hypothesis in \(\mathbb{R}^3\). In particular, this limit is a weak solution of the corresponding Euler equations. We first deduce the Kolmogorov-type hypothesis in \(\mathbb{R}^3\), which yields the uniform bounds of \(\alpha^{th}\)-order fractional derivatives of \(\sqrt{\rho^\mu} \mathbf{u}^\mu\) in \(L^2_x\) for some \(\alpha > 0\), independent of the viscosity. The uniform bounds can provide strong convergence of \(\sqrt{\rho^\mu} \mathbf{u}^\mu\) in \(L^2\) space. This shows that the inviscid limit is a weak solution to the corresponding Euler equations.Global well-posedness and time-decay estimates for compressible Navier-Stokes equations with reaction diffusionhttps://zbmath.org/1491.353232022-09-13T20:28:31.338867Z"Wang, Wenjun"https://zbmath.org/authors/?q=ai:wang.wenjun"Wen, Huanyao"https://zbmath.org/authors/?q=ai:wen.huanyaoSummary: We consider the full compressible Navier-Stokes equations with reaction diffusion. A global existence and uniqueness result of the strong solution is established for the Cauchy problem when the initial data is in a neighborhood of a trivially stationary solution. The appearance of the difference between energy gained and energy lost due to the reaction is a new feature for the flow and brings new difficulties. To handle these, we construct a new linearized system in terms of a combination of the solutions. Moreover, some optimal time-decay estimates of the solutions are derived when the initial perturbation is additionally bounded in \(L^1\). It is worth noticing that there is no decay loss for the highest-order spatial derivatives of the solution so that the long time behavior for the hyperbolic-parabolic system is exactly the same as that for the heat equation. As a byproduct, the above time-decay estimate at the highest order is also valid for compressible Navier-Stokes equations. The proof is accomplished by virtue of Fourier theory and a new observation for cancellation of a low-medium-frequency quantity.Partially regular weak solutions of the stationary Navier-Stokes equations in dimension 6https://zbmath.org/1491.353242022-09-13T20:28:31.338867Z"Wu, Bian"https://zbmath.org/authors/?q=ai:wu.bianSummary: By using defect measures, we prove the existence of partially regular weak solutions to the stationary Navier-Stokes equations with external force \(f \in L_{\mathrm{loc}}^q \cap L^{3/2}\), \(q>3\) in general open subdomains of \(\mathbb{R}^6\). These weak solutions satisfy certain local energy estimates and we estimate the size of their singular sets in terms of Hausdorff measures. We also prove the defect measures vanish under a smallness condition, in contrast to the nonstationary Navier-Stokes equations in \(\mathbb{R}^4 \times [0, \infty[\).Global solutions to 3D incompressible Navier-Stokes equations with some large initial datahttps://zbmath.org/1491.353252022-09-13T20:28:31.338867Z"Yu, Yanghai"https://zbmath.org/authors/?q=ai:yu.yanghai"Li, Jinlu"https://zbmath.org/authors/?q=ai:li.jinlu.1"Yin, Zhaoyang"https://zbmath.org/authors/?q=ai:yin.zhaoyangSummary: In this paper, we derive a new smallness hypothesis of initial data for the three-dimensional incompressible Navier-Stokes equations. More precisely, we prove that if
\[
\begin{aligned}
\Bigg(&\| u_0^1 + u_0^2 \|_{\dot{B}_{p, 1}^{\frac{ 3}{ p} - 1}} + \| u_0^3 \|_{\dot{B}_{p, 1}^{\frac{ 3}{ p} - 1}}\Bigg) \Bigg(\| u_0^1 \|_{\dot{B}_{p, 1}^{\frac{ 3}{ p} - 1}} + \| u_0^2 \|_{\dot{B}_{p, 1}^{\frac{ 3}{ p} - 1}}\Bigg)\\
&\times \exp \Bigg(C \Big(\| u_0 \|_{\dot{B}_{\infty, 2}^{- 1}}^2 + \| u_0 \|_{\dot{B}_{\infty, 1}^{- 1}} \Big)\Bigg)
\end{aligned}
\]
is small enough, the Navier-Stokes equations have a unique global solution. As an application, we construct two examples of initial data satisfying the smallness condition, but whose \(\dot{B}_{\infty, \infty}^{- 1} (\mathbb{R}^3)\) norm can be arbitrarily large.Rayleigh-Taylor instability for viscous incompressible capillary fluidshttps://zbmath.org/1491.353262022-09-13T20:28:31.338867Z"Zhang, Zhipeng"https://zbmath.org/authors/?q=ai:zhang.zhipengSummary: We investigate the linear and nonlinear instability of a smooth Rayleigh-Taylor steady state solution to the three-dimensional incompressible Navier-Stokes-Korteweg equations in the presence of a uniform gravitational field. We first analyze the linearized equations around the steady state solution and find that for any capillary coefficient \(\kappa >0\), we can construct the solutions of the linearized problem that grow in time in Sobolev space \(H^m\), thus leading to the linear instability. However, with the help of the constructed unstable solutions of the linearized problem, we just establish the nonlinear instability for small enough capillary coefficient \(\kappa >0\).Conjugate points in \(\mathcal{D}_\mu^s(S^2)\)https://zbmath.org/1491.353272022-09-13T20:28:31.338867Z"Benn, J."https://zbmath.org/authors/?q=ai:benn.jamesSummary: Rossby-Haurwitz waves on the sphere \(S^2\) form a set of exact time-dependent solutions to the Euler equations of hydrodynamics and generate a family of non-stationary geodesics of the \(L^2\) metric in the volume preserving diffeomorphism group of \(S^2\). Restricting to a particular subset of Rossby-Haurwitz waves, this article shows that under certain conditions on the physical characteristics of the waves each corresponding geodesic contains conjugate points. In addition, a physical interpretation of conjugate points is given and links the result to the stability analysis of meteorological Rossby-Haurwitz waves.Nonlinear stability of planar steady Euler flows associated with semistable solutions of elliptic problemshttps://zbmath.org/1491.353282022-09-13T20:28:31.338867Z"Wang, Guodong"https://zbmath.org/authors/?q=ai:wang.guodongSummary: This paper is devoted to the study of nonlinear stability of steady incompressible Euler flows in two dimensions. We prove that a steady Euler flow is nonlinearly stable in \(L^p\) norm of the vorticity if its stream function is a semistable solution of some semilinear elliptic problem with nondecreasing nonlinearity. The idea of the proof is to show that such a flow has strict local maximum energy among flows whose vorticities are rearrangements of a given function, with the help of an improved version of Wolansky and Ghil's stability theorem. The result can be regarded as an extension of Arnol'd's second stability theorem.On a higher integral invariant for closed magnetic lines, revisitedhttps://zbmath.org/1491.353292022-09-13T20:28:31.338867Z"Akhmet'ev, Peter M."https://zbmath.org/authors/?q=ai:akhmetev.petr-mSummary: We recall a definition of an asymptotic invariant of classical link, which is called \(M\)-invariant. \(M\)-invariant is a special Massey integral, this integral has an ergodic form and is generalized for magnetic fields with open magnetic lines in a bounded \(3D\)-domain. We present a proof that this integral is well defined. A combinatorial formula for \(M\)-invariant using the Conway polynomial is presented. The \(M\)-invariant is a higher invariant, it is not a function of pairwise linking numbers of closed magnetic lines. We discuss applications of \(M\)-invariant for MHD.Well-posedness and blow-up of solutions for the 2D dissipative quasi-geostrophic equation in critical Fourier-Besov-Morrey spaceshttps://zbmath.org/1491.353302022-09-13T20:28:31.338867Z"Azanzal, Achraf"https://zbmath.org/authors/?q=ai:azanzal.achraf"Allalou, Chakir"https://zbmath.org/authors/?q=ai:allalou.chakir"Melliani, Said"https://zbmath.org/authors/?q=ai:melliani.saidSummary: This paper establishes the existence and uniqueness, and also presents a blow-up criterion, for solutions of the quasi-geostrophic (QG) equation in a framework of Fourier type, specifically Fourier-Besov-Morey spaces. If it is assumed that the initial data \(\theta_0\) is small and belonging to the critical Fourier-Besov-Morrey spaces \(\mathscr{F} {\mathscr{N}}_{p, \lambda, q}^{3-2 \alpha +\frac{\lambda -2}{p}} \), we get the global well-posedness results of the QG equation (1). Moreover, we prove that there exists a time \(T > 0\) such that the QG equation (1) admits a unique local solution for large initial data.Mixing solutions for the Muskat problemhttps://zbmath.org/1491.353312022-09-13T20:28:31.338867Z"Castro, A."https://zbmath.org/authors/?q=ai:castro.angel"Córdoba, D."https://zbmath.org/authors/?q=ai:cordoba.diego"Faraco, D."https://zbmath.org/authors/?q=ai:faraco.danielSummary: We prove the existence of mixing solutions of the incompressible porous media equation for all Muskat type \(H^5\) initial data in the fully unstable regime. The proof combines convex integration, contour dynamics and a basic calculus for non smooth semiclassical type pseudodifferential operators which is developed.Hamiltonian description of internal ocean waves with Coriolis forcehttps://zbmath.org/1491.353322022-09-13T20:28:31.338867Z"Cullen, Joseph D."https://zbmath.org/authors/?q=ai:cullen.joseph-d"Ivanov, Rossen I."https://zbmath.org/authors/?q=ai:ivanov.rossen-iSummary: The interfacial internal waves are formed at the pycnocline or thermocline in the ocean and are influenced by the Coriolis force due to the Earth's rotation. A derivation of the model equations for the internal wave propagation taking into account the Coriolis effect is proposed. It is based on the Hamiltonian formulation of the internal wave dynamics in the irrotational case, appropriately extended to a nearly Hamiltonian formulation which incorporates the Coriolis forces. Two propagation regimes are examined, the long-wave and the intermediate long-wave propagation with a small amplitude approximation for certain geophysical scales of the physical variables. The obtained models are of the type of the well-known Ostrovsky equation and describe the wave propagation over the two spatial horizontal dimensions of the ocean surface.On uniqueness and helicity conservation of weak solutions to the electron-MHD systemhttps://zbmath.org/1491.353332022-09-13T20:28:31.338867Z"Dai, Mimi"https://zbmath.org/authors/?q=ai:dai.mimi"Krol, Jacob"https://zbmath.org/authors/?q=ai:krol.jacob"Liu, Han"https://zbmath.org/authors/?q=ai:liu.hanSummary: We study weak solutions to the electron-MHD system and obtain a conditional uniqueness result. In addition, we prove conservation of helicity for weak solutions to the electron-MHD system under a geometric condition.Travelling waves in the Boussinesq type systemshttps://zbmath.org/1491.353342022-09-13T20:28:31.338867Z"Dinvay, Evgueni"https://zbmath.org/authors/?q=ai:dinvay.evgueniSummary: Considered herein are a number of variants of the Boussinesq type systems modelling surface water waves. Such equations were derived by different authors to describe the two-way propagation of long gravity waves. A question of existence of special solutions, the so called solitary waves, is of a particular interest. There are a number of studies relying on a variational approach and a concentration-compactness argument. These proofs are technically very demanding and may vary significantly from one system to another. Our approach is based on the implicit function theorem, which makes the treatment easier and more unified.Uniform regularity for a density-dependent incompressible Hall-MHD systemhttps://zbmath.org/1491.353352022-09-13T20:28:31.338867Z"Fan, Jishan"https://zbmath.org/authors/?q=ai:fan.jishan"Zhou, Yong"https://zbmath.org/authors/?q=ai:zhou.yong.1Summary: This paper proves uniform regularity for a density-dependent incompressible Hall-MHD system with positive density.Energy considerations for nonlinear equatorial water waveshttps://zbmath.org/1491.353362022-09-13T20:28:31.338867Z"Henry, David"https://zbmath.org/authors/?q=ai:henry.david.2|henry.david.1Summary: In this article we consider the excess kinetic and potential energies for exact nonlinear equatorial water waves. An investigation of linear waves establishes that the excess kinetic energy density is always negative, whereas the excess potential energy density is always positive, for periodic travelling irrotational water waves in the steady reference frame. For negative wavespeeds, we prove that similar inequalities must also hold for nonlinear wave solutions. Characterisations of the various excess energy densities as integrals along the wave surface profile are also derived.Continued gravitational collapse for gaseous star and pressureless Euler-Poisson systemhttps://zbmath.org/1491.353372022-09-13T20:28:31.338867Z"Huang, Feimin"https://zbmath.org/authors/?q=ai:huang.feimin"Yao, Yue"https://zbmath.org/authors/?q=ai:yao.yueGlobal well-posedness of classical solutions to the Cauchy problem of two-dimensional barotropic compressible Navier-Stokes system with vacuum and large initial datahttps://zbmath.org/1491.353382022-09-13T20:28:31.338867Z"Huang, Xiangdi"https://zbmath.org/authors/?q=ai:huang.xiangdi"Li, Jing"https://zbmath.org/authors/?q=ai:li.jingOptimal decay for the 3D anisotropic Boussinesq equations near the hydrostatic balancehttps://zbmath.org/1491.353392022-09-13T20:28:31.338867Z"Ji, Ruihong"https://zbmath.org/authors/?q=ai:ji.ruihong"Yan, Li"https://zbmath.org/authors/?q=ai:yan.li"Wu, Jiahong"https://zbmath.org/authors/?q=ai:wu.jiahongSummary: This paper focuses on the three-dimensional (3D) incompressible anisotropic Boussinesq system with horizontal dissipation. The goal here is to assess the stability property and pinpoint the precise large-time behavior of perturbations near the hydrostatic balance. Important tools such as Schonbek's Fourier splitting method have been developed to understand the large-time behavior of PDE systems with full dissipation, but these tools may not apply directly when the systems are only partially dissipated. This paper solves the stability problem and designs an effective approach to obtain the optimal decay rates for the anisotropic Boussinesq system concerned here. The tool developed in this paper may be useful for many other partially dissipated systems.Mixed methods for the velocity-pressure-pseudostress formulation of the Stokes eigenvalue problemhttps://zbmath.org/1491.353402022-09-13T20:28:31.338867Z"Lepe, Felipe"https://zbmath.org/authors/?q=ai:lepe.felipe"Rivera, Gonzalo"https://zbmath.org/authors/?q=ai:rivera.gonzalo"Vellojin, Jesus"https://zbmath.org/authors/?q=ai:vellojin.jesusOrbital stability of the sum of smooth solitons in the Degasperis-Procesi equationhttps://zbmath.org/1491.353412022-09-13T20:28:31.338867Z"Li, Ji"https://zbmath.org/authors/?q=ai:li.ji.2"Liu, Yue"https://zbmath.org/authors/?q=ai:liu.yue"Wu, Qiliang"https://zbmath.org/authors/?q=ai:wu.qiliangSummary: The Degasperis-Procesi (DP) equation is an integrable Camassa-Holm-type model as an asymptotic approximation for the unidirectional propagation of shallow water waves. This work is to establish the \(L^2 \cap L^\infty\) orbital stability of a wave train containing \(N\) smooth solitons which are well separated. The main difficulties stem from the subtle nonlocal structure of the DP equation. One consequence is that the energy space of the DE equation based on the conserved quantity induced by the translation symmetry is only equivalent to the \(L^2\)-norm, which by itself can not bound the higher-order nonlinear terms in the Lagrangian. Our remedy is to introduce \textit{a priori} estimates based on certain smooth initial conditions. Moreover, another consequence is that the nonlocal structure of the DP equation significantly complicates the verification of the monotonicity of local momentum and the positive definiteness of a refined quadratic form of the orthogonalized perturbation.On the effect of fast rotation and vertical viscosity on the lifespan of the \(3D\) Primitive equationshttps://zbmath.org/1491.353422022-09-13T20:28:31.338867Z"Lin, Quyuan"https://zbmath.org/authors/?q=ai:lin.quyuan"Liu, Xin"https://zbmath.org/authors/?q=ai:liu.xin.5|liu.xin.3|liu.xin.2|liu.xin|liu.xin.4|liu.xin.1"Titi, Edriss S."https://zbmath.org/authors/?q=ai:titi.edriss-salehSummary: We study the effect of the fast rotation and vertical viscosity on the lifespan of solutions to the three-dimensional primitive equations (also known as the hydrostatic Navier-Stokes equations) with impermeable and stress-free boundary conditions. Firstly, for a short time interval, independent of the rate of rotation \(|\Omega|\), we establish the local well-posedness of solutions with initial data that is analytic in the horizontal variables and only \(L^2\) in the vertical variable. Moreover, it is shown that the solutions immediately become analytic in all the variables with increasing-in-time (at least linearly) radius of analyticity in the vertical variable for as long as the solutions exist. On the other hand, the radius of analyticity in the horizontal variables might decrease with time, but as long as it remains positive the solution exists. Secondly, with fast rotation, i.e., large \(|\Omega|\), we show that the existence time of the solution can be prolonged, with ``well-prepared'' initial data. Finally, in the case of two spatial dimensions with \(\Omega =0\), we establish the global well-posedness provided that the initial data is small enough. The smallness condition on the initial data depends on the vertical viscosity and the initial radius of analyticity in the horizontal variables.Global well-posedness of 3d axisymmetric MHD-Boussinesq system with nonzero swirlhttps://zbmath.org/1491.353432022-09-13T20:28:31.338867Z"Liu, Qiao"https://zbmath.org/authors/?q=ai:liu.qiao"Yang, Yixin"https://zbmath.org/authors/?q=ai:yang.yixinSummary: In this paper, we consider the 3d axisymmetric MHD-Boussinesq system with nonzero swirl, and prove that the system, with initial data \((u_0, h_0, \rho_0) = (u^r_0 e_r + u^\theta_0 e_\theta + u^z_0 e_z, h^\theta_0 e_\theta, \rho_0)\) which satisfies some small nonlinear condition, admits a global unique solution \((u, h, \rho)\). Furthermore, some continuation criteria that imply regularity of axisymmetric solutions are also obtained.Instantaneous smoothing and exponential decay of solutions for a degenerate evolution equation with application to Boltzmann's equationhttps://zbmath.org/1491.353442022-09-13T20:28:31.338867Z"Nazarov, Fedor"https://zbmath.org/authors/?q=ai:nazarov.fedor-l"Zumbrun, Kevin"https://zbmath.org/authors/?q=ai:zumbrun.kevin-rSummary: We establish an instantaneous smoothing property for decaying solutions on the half-line \((0, +\infty)\) of certain degenerate Hilbert space-valued evolution equations arising in kinetic theory, including in particular the steady Boltzmann equation. Our results answer the two main open problems posed by Pogan and Zumbrun in their treatment of \(H^1\) stable manifolds of such equations, showing that \(L^2_{loc}\) solutions that remain sufficiently small in \(L^\infty\) (i) decay exponentially, and (ii) are \(C^\infty\) for \(t>0 \), hence lie eventually in the \(H^1\) stable manifold constructed by Pogan and Zumbrun.Global existence in critical spaces for non Newtonian compressible viscoelastic flowshttps://zbmath.org/1491.353452022-09-13T20:28:31.338867Z"Pan, Xinghong"https://zbmath.org/authors/?q=ai:pan.xinghong"Xu, Jiang"https://zbmath.org/authors/?q=ai:xu.jiang"Zhu, Yi"https://zbmath.org/authors/?q=ai:zhu.yi|zhu.yi.1|zhu.yi.3|zhu.yi.2Summary: We are interested in the multi-dimensional compressible viscoelastic flows of Oldroyd type, which is one of non-Newtonian fluids exhibiting the elastic behavior. In order to capture the damping effect of the additional deformation tensor, to the best of our knowledge, the ``div-curl'' structural condition plays a key role in previous efforts. Our aim of this paper is to remove the structural condition and prove a global existence of strong solutions to compressible viscoelastic flows in critical spaces. In absence of compatible conditions, the new effective flux is introduced, which enables us to capture the dissipation arising from \textit{combination} of density and deformation tensor. The partial dissipation in non-Newtonian compressible fluids, is weaker than that of classical Navier-Stokes equations.A ternary Cahn-Hilliard-Navier-Stokes model for two-phase flow with precipitation and dissolutionhttps://zbmath.org/1491.353462022-09-13T20:28:31.338867Z"Rohde, Christian"https://zbmath.org/authors/?q=ai:rohde.christian"von Wolff, Lars"https://zbmath.org/authors/?q=ai:von-wolff.larsSharp convergence rates for Darcy's lawhttps://zbmath.org/1491.353472022-09-13T20:28:31.338867Z"Shen, Zhongwei"https://zbmath.org/authors/?q=ai:shen.zhongwei.1|shen.zhongweiSummary: This article is concerned with Darcy's law for an incompressible viscous fluid flowing in a porous medium. We establish the sharp \(O(\sqrt{\varepsilon})\) convergence rate in a periodically perforated and bounded domain in \(\mathbb{R}^d\) for \(d\geq 2\), where \(\varepsilon\) represents the size of solid obstacles. This is achieved by constructing two boundary layer correctors to control the boundary layers created by the incompressibility condition and the discrepancy of boundary values between the solution and the leading term in its asymptotic expansion. One of the correctors deals with the tangential boundary data, while the other handles the normal boundary data.Compactness and large-scale regularity for Darcy's lawhttps://zbmath.org/1491.353482022-09-13T20:28:31.338867Z"Shen, Zhongwei"https://zbmath.org/authors/?q=ai:shen.zhongwei|shen.zhongwei.1Summary: This paper is concerned with the quantitative homogenization of the steady Stokes equations with the Dirichlet condition in a periodically perforated domain. Using a compactness method, we establish the large-scale interior \(C^{1,\alpha}\) and Lipschitz estimates for the velocity as well as the corresponding estimates for the pressure. These estimates, when combined with the classical regularity estimates for the Stokes equations, yield the uniform Lipschitz estimates. As a consequence, we also obtain the uniform \(W^{k,p}\) estimates for \(1<p<\infty\).The MHD equations in the Lorentz space with time dependent external forceshttps://zbmath.org/1491.353492022-09-13T20:28:31.338867Z"Tan, Zhong"https://zbmath.org/authors/?q=ai:tan.zhong"Zhou, Jianfeng"https://zbmath.org/authors/?q=ai:zhou.jianfengSummary: We are concerned with the well-posedness of the incompressible Magneto-hydrodynamical (MHD) equations in \(\mathbb{R}^n\) (\(n\ge 3\)). First, by assuming the smallness of the external force in Lorentz spaces, we prove the existence, uniqueness and the time regularity of periodic mild solution of an integral form of MHD Eqs. (1.1). Next, we prove the local existence and uniqueness of mild solution of the Cauchy problem of MHD Eqs. (1.2). Finally, appealing to the existence and uniqueness of the mild solution of (1.2), we show that the obtained solution \((u, b)\) of (1.1) becomes the time periodic strong solution, derived from the strong solvability of the inhomogeneous Stokes equation and heat equation by an additional assumption of the external force.Inexact GMRES iterations and relaxation strategies with fast-multipole boundary element methodhttps://zbmath.org/1491.353502022-09-13T20:28:31.338867Z"Wang, Tingyu"https://zbmath.org/authors/?q=ai:wang.tingyu"Layton, Simon K."https://zbmath.org/authors/?q=ai:layton.simon-k"Barba, Lorena A."https://zbmath.org/authors/?q=ai:barba.lorena-aSummary: Boundary element methods produce dense linear systems that can be accelerated via multipole expansions. Solved with Krylov methods, this implies computing the matrix-vector products within each iteration with some error, at an accuracy controlled by the order of the expansion, \(p\). We take advantage of a unique property of Krylov iterations that allows lower accuracy of the matrix-vector products as convergence proceeds, and propose a relaxation strategy based on progressively decreasing \(p\). In extensive numerical tests of the relaxed Krylov iterations, we obtained speed-ups of between \(1.5 \times\) and \(2.3 \times\) for Laplace problems and between \(2.7 \times\) and \(3.3 \times\) for Stokes problems. We include an application to Stokes flow around red blood cells, computing with up to 64 cells and problem size up to 131k boundary elements and nearly 400k unknowns. The study was done with an in-house multi-threaded C++ code, on a hexa-core CPU. The code is available on its version-control repository, \url{https://github.com/barbagroup/fmm-bem-relaxed}, and we share reproducibility packages for all results in \url{https://github.com/barbagroup/inexact-gmres/}.A stochastic approach to enhanced diffusionhttps://zbmath.org/1491.353512022-09-13T20:28:31.338867Z"Zelati, Michele Coti"https://zbmath.org/authors/?q=ai:coti-zelati.michele"Drivas, Theodore D."https://zbmath.org/authors/?q=ai:drivas.theodore-dSummary: We provide examples of initial data which saturate the enhanced diffusion rates proved for general shear flows which are Hölder regular or Lipschitz continuous with critical points, and for regular circular flows, establishing the sharpness of those results. Our proof makes use of a probabilistic interpretation of the dissipation of solutions to the advection diffusion equation.Delta waves and vacuum states in the vanishing pressure limit of Riemann solutions to Baer-Nunziato two-phase flow modelhttps://zbmath.org/1491.353522022-09-13T20:28:31.338867Z"Zhang, Qinglong"https://zbmath.org/authors/?q=ai:zhang.qinglongSummary: The phenomena of concentration and cavitation for the Riemann problem of the Baer-Nunziato (BN) two-phase flow model has been investigated in this paper. By using the characteristic analysis method, the formation of \(\delta\)-waves and vacuum states are obtained as the pressure for both phases vanish in the BN model. The solid contact wave is carefully dealt. The comparison with the solutions of pressureless two-phase model shows that, two shock waves tend to a \(\delta\)-shock solution, and two rarefaction waves tend to a two contact discontinuity solution when the solid contact discontinuity is involved. Moreover, the detailed Riemann solutions for two-phase flow model are given as the double pressure parameters vanish. This may contribute to the design of numerical schemes in the future research.Stabilization and exponential decay for 2D Boussinesq equations with partial dissipationhttps://zbmath.org/1491.353532022-09-13T20:28:31.338867Z"Zhong, Yueyuan"https://zbmath.org/authors/?q=ai:zhong.yueyuanSummary: This paper focuses on a special 2D Boussinesq equation with partial dissipation, for which the velocity equation involves no dissipation and there is only damping in the horizontal component equation. Without buoyancy force, the corresponding vorticity equation is a 2D Euler-like equation with an extra Calderon-Zygmund-type term. Its stability is an open problem. Our results reveal that the buoyancy force exactly stabilizes the fluids by the coupling and interaction between the velocity and temperature. In addition, we prove the solution decays exponentially to zero in Sobolev norm.Convergence toward the steady state of a collisionless gas with Cercignani-Lampis boundary conditionhttps://zbmath.org/1491.353802022-09-13T20:28:31.338867Z"Bernou, Armand"https://zbmath.org/authors/?q=ai:bernou.armandSummary: We study the asymptotic behavior of the kinetic free-transport equation enclosed in a regular domain, on which no symmetry assumption is made, with Cercignani-Lampis boundary condition. We give the first proof of existence of a steady state in the case where the temperature at the wall varies, and derive the optimal rate of convergence toward it, in the \(L^1\) norm. The strategy is an application of a deterministic version of Harris' subgeometric theorem, in the spirit of the recent results of Cañizo-Mischler and of the previous study of Bernou. We also investigate rigorously the velocity flow of a model mixing pure diffuse and Cercignani-Lampis boundary conditions with variable temperature, for which we derive an explicit form for the steady state, providing new insights on the role of the Cercignani-Lampis boundary condition in this problem.Transport equations with inflow boundary conditionshttps://zbmath.org/1491.353862022-09-13T20:28:31.338867Z"Scott, L. Ridgway"https://zbmath.org/authors/?q=ai:scott.larkin-ridgway"Pollock, Sara"https://zbmath.org/authors/?q=ai:pollock.saraSummary: We provide bounds in a Sobolev-space framework for transport equations with nontrivial inflow and outflow. We give, for the first time, bounds on the gradient of the solution with the type of inflow boundary conditions that occur in Poiseuille flow. Following ground-breaking work of the late \textit{C. J. Amick} [Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 4, 473--513 (1977; Zbl 0367.76027)], we name a generalization of this type of flow domain in his honor. We prove gradient bounds in Lebesgue spaces for general Amick domains which are crucial for proving well posedness of the grade-two fluid model. We include a complete review of transport equations with inflow boundary conditions, providing novel proofs in most cases. To illustrate the theory, we review and extend an example of Bernard that clarifies the singularities of solutions of transport equations with nonzero inflow boundary conditions.Time-fractional Moore-Gibson-Thompson equationshttps://zbmath.org/1491.354332022-09-13T20:28:31.338867Z"Kaltenbacher, Barbara"https://zbmath.org/authors/?q=ai:kaltenbacher.barbara"Nikolić, Vanja"https://zbmath.org/authors/?q=ai:nikolic.vanjaThe non-Lipschitz stochastic Cahn-Hilliard-Navier-Stokes equations in two space dimensionshttps://zbmath.org/1491.354702022-09-13T20:28:31.338867Z"Sun, Chengfeng"https://zbmath.org/authors/?q=ai:sun.chengfeng"Huang, Qianqian"https://zbmath.org/authors/?q=ai:huang.qianqian"Liu, Hui"https://zbmath.org/authors/?q=ai:liu.hui.3|liu.hui.2|liu.hui.1|liu.hui.4Large deviation principles for a 2D stochastic Allen-Cahn-Navier-Stokes driven by jump noisehttps://zbmath.org/1491.354712022-09-13T20:28:31.338867Z"Tachim Medjo, Theodore"https://zbmath.org/authors/?q=ai:tachim-medjo.theodoreErgodic theory for energetically open compressible fluid flowshttps://zbmath.org/1491.370042022-09-13T20:28:31.338867Z"Fanelli, Francesco"https://zbmath.org/authors/?q=ai:fanelli.francesco"Feireisl, Eduard"https://zbmath.org/authors/?q=ai:feireisl.eduard"Hofmanová, Martina"https://zbmath.org/authors/?q=ai:hofmanova.martinaSummary: The ergodic hypothesis is examined for energetically open fluid systems represented by the barotropic Navier-Stokes equations with general inflow/outflow boundary conditions. We show that any globally bounded trajectory generates a stationary statistical solution, which is interpreted as a stochastic process with continuous trajectories supported by the family of weak solutions of the problem. The abstract Birkhoff-Khinchin theorem is applied to obtain convergence (in expectation and a.s.) of ergodic averages for any bounded Borel measurable function of state variables associated to any stationary solution. Finally, we show that validity of the ergodic hypothesis is determined by the behavior of entire solutions (i.e. a solution defined for any \(t \in R\)). In particular, the ergodic averages converge for \textit{any} trajectory provided its \(\omega\)-limit set in the trajectory space supports a unique (in law) stationary solution.Emergent behaviors of relativistic flocks on Riemannian manifoldshttps://zbmath.org/1491.370772022-09-13T20:28:31.338867Z"Ahn, Hyunjin"https://zbmath.org/authors/?q=ai:ahn.hyunjin"Ha, Seung-Yeal"https://zbmath.org/authors/?q=ai:ha.seung-yeal"Kang, Myeongju"https://zbmath.org/authors/?q=ai:kang.myeongju"Shim, Woojoo"https://zbmath.org/authors/?q=ai:shim.woojooSummary: We present a relativistic counterpart of the Cucker-Smale (CS) model on Riemannian manifolds (manifold RCS model in short) and study its collective behavior. For Euclidean space, the \textit{relativistic Cucker-Smale} (RCS) model was introduced in [\textit{S.-Y. Ha} et al., Arch. Ration. Mech. Anal. 235, No. 3, 1661--1706 (2020; Zbl 1439.35397)] via the method of a rational reduction from the relativistic gas mixture equations by assuming space-homogeneity, suitable ansatz for entropy and principle of subsystem. In this work, we extend the RCS model on Euclidean space to connected, complete and smooth Riemannian manifolds by replacing usual time derivative of velocity and relative velocity by suitable geometric quantities such as covariant derivative and parallel transport along length-minimizing geodesics. For the proposed model, we present a Lyapunov functional which decreases monotonically on generic manifolds, and show the emergence of weak velocity alignment on compact manifolds by using LaSalle's invariance principle. As concrete examples, we further analyze the RCS models on the unit sphere \(\mathbb{S}^d\) and the hyperbolic space \(\mathbb{H}^d\). More precisely, we show that the RCS model on \(\mathbb{S}^d\) exhibits a dichotomy in asymptotic spatial patterns, and provide a sufficient framework leading to the velocity alignment of RCS particles in \(\mathbb{H}^d\). For the hyperbolic space \(\mathbb{H}^d\), we also rigorously justify smooth transition from the RCS model to the CS model in any finite time interval, as speed of light tends to infinity.Nonlinear approximation of 3D smectic liquid crystals: sharp lower bound and compactnesshttps://zbmath.org/1491.490112022-09-13T20:28:31.338867Z"Novack, Michael"https://zbmath.org/authors/?q=ai:novack.michael-r"Yan, Xiaodong"https://zbmath.org/authors/?q=ai:yan.xiaodongSummary: We consider the 3D smectic energy
\[
\mathcal{E}_\varepsilon(u) = \frac{1}{2}\int_\Omega \frac{1}{\varepsilon} \left( \partial_z u-\frac{(\partial_x u)^2+(\partial_y u)^2}{2}\right)^2 +\varepsilon \left(\partial_x^2u + \partial_y^2u\right)^2dx\,dy\,dz.
\]
The model contains as a special case the well-known 2D Aviles-Giga model. We prove a sharp lower bound on \(\mathcal{E}_\varepsilon\) as \(\varepsilon \rightarrow 0\) by introducing 3D analogues of the Jin-Kohn entropies [\textit{W. Jin} and \textit{R. V. Kohn}, J. Nonlinear Sci. 10, No. 3, 355--390 (2000; Zbl 0973.49009)]. The sharp bound corresponds to an equipartition of energy between the bending and compression strains and was previously demonstrated in the physics literature only when the approximate Gaussian curvature of each smectic layer vanishes. Also, for \(\varepsilon_n\rightarrow 0\) and an energy-bounded sequence \(\{u_n\}\) with \(\Vert\nabla u_n\Vert_{L^p(\Omega)}\), \(\Vert \nabla u_n\Vert_{L^2(\partial\Omega)}\le C\) for some \(p>6\), we obtain compactness of \(\nabla u_n\) in \(L^2\) assuming that \(\Delta_{xy}u_n\) has constant sign for each \(n\).The measurement and analysis of shapes. An application of hydrodynamics and probability theoryhttps://zbmath.org/1491.580022022-09-13T20:28:31.338867Z"Benn, James"https://zbmath.org/authors/?q=ai:benn.james"Marsland, Stephen"https://zbmath.org/authors/?q=ai:marsland.stephen-rSummary: A de Rham \(p\)-current can be viewed as a map (the current map) between the set of embeddings of a closed \(p\)-dimensional manifold into an ambient \(n\)-manifold and the set of linear functionals on differential \(p\)-forms. We demonstrate that, for suitably chosen Sobolev topologies on both the space of embeddings and the space of \(p\)-forms, the current map is continuously differentiable, with an image that consists of bounded linear functionals on \(p\)-forms. Using the Riesz representation theorem, we prove that each \(p\)-current can be represented by a unique co-exact differential form that has a particular interpretation depending on \(p\). Embeddings of a manifold can be thought of as shapes with a prescribed topology. Our analysis of the current map provides us with representations of shapes that can be used for the measurement and statistical analysis of collections of shapes. We consider two special cases of our general analysis and prove that: (1) if \(p=n-1\) then closed, embedded, co-dimension one surfaces are naturally represented by probability distributions on the ambient manifold and (2) if \(p=1\) then closed, embedded, one-dimensional curves are naturally represented by fluid flows on the ambient manifold. In each case, we outline some statistical applications using an \({\dot{H}}^1\) and \(L^2\) metric, respectively.Kolmogorov's theory of turbulence and its rigorous 1d modelhttps://zbmath.org/1491.601032022-09-13T20:28:31.338867Z"Kuksin, Sergei"https://zbmath.org/authors/?q=ai:kuksin.sergei-bThe author summarizes the main results (with some sketched proofs) of the book [One-dimensional turbulence and the stochastic Burgers equation. Providence, RI: American Mathematical Society (AMS) (2021; Zbl 1486.60002)] coauthored with \textit{A. Boritchev} and \textit{S. Kuksin}. The author considers the 1D viscous Burgers equation with periodic boundary condition and additive noise which is spatially smooth. When the viscosity is small enough (equivalently, the Reynolds number is sufficiently big), he is able to rigorously estimate some quantities like dissipation scale, structure function and energy spectrum; the purpose is to compare these quantities with the predictions of Kolmogorov's turbulence theory, abbreviated as the K41 theory. The author concludes that the statistical properties of stochastic 1D Burgers equation with small viscosity are close analogues of the main laws of the K41 theory, which supports the belief that K41 theory is ``close to the truth''.
Reviewer: Dejun Luo (Beijing)Comparison of gradient approximation methods in schemes designed for scale-resolving simulationshttps://zbmath.org/1491.650222022-09-13T20:28:31.338867Z"Bakhné, S."https://zbmath.org/authors/?q=ai:bakhne.s"Bosnyakov, S. M."https://zbmath.org/authors/?q=ai:bosnyakov.s-m"Mikhaĭlov, S. V."https://zbmath.org/authors/?q=ai:mikhailov.s-v"Troshin, A. I."https://zbmath.org/authors/?q=ai:troshin.a-iSummary: Various methods for improved accuracy approximation of the gradients entering the diffusion fluxes are considered. Linear combinations of 2nd order difference schemes for a non-uniform grid that transform into 4th order schemes in the uniform case were investigated. We also considered 3rd and 4th order schemes for approximating gradients on a non-uniform grid in the normal and tangent directions to the cell face, respectively, based on Lagrange polynomials. The initial testing was carried out on one-dimensional functions: a smooth Gauss function and a piecewise linear function. Next, the schemes were applied in direct numerical simulation of the Taylor-Green vortex.Augmented upwind numerical schemes for a fractional advection-dispersion equation in fractured groundwater systemshttps://zbmath.org/1491.650772022-09-13T20:28:31.338867Z"Allwright, Amy"https://zbmath.org/authors/?q=ai:allwright.amy"Atangana, Abdon"https://zbmath.org/authors/?q=ai:atangana.abdonSummary: The anomalous transport of particles within non-linear systems cannot be captured accurately with the classical advection-dispersion equation, due to its inability to incorporate non-linearity of geological formations in the mathematical formulation. Fortunately, fractional differential operators have been recognised as appropriate mathematical tools to describe such natural phenomena. The classical advection-dispersion equation is adapted to a fractional model by replacing the time differential operator by a time fractional derivative to include the power-law waiting time distribution. The advection component is adapted by replacing the local differential by a fractional space derivative to account for mean-square displacement from normal to super-advection. Due to the complexity of this new model, new numerical schemes are suggested, including an upwind Crank-Nicholson and weighted upwind-downwind scheme. Both numerical schemes are used to solve the modified fractional advection-dispersion model and the conditions of their stability established.Non-overlapping Schwarz algorithms for the incompressible Navier-Stokes equations with DDFV discretizationshttps://zbmath.org/1491.650812022-09-13T20:28:31.338867Z"Goudon, Thierry"https://zbmath.org/authors/?q=ai:goudon.thierry"Krell, Stella"https://zbmath.org/authors/?q=ai:krell.stella"Lissoni, Giulia"https://zbmath.org/authors/?q=ai:lissoni.giuliaThe authors consider the numerical resolution of the unsteady incompressible Navier-Stokes problem. They first establish the well-posedness of DDFV (Discrete Duality Finite Volume) schemes on the whole spatial domain with general convection fluxes defined by \(B\)-schemes. Subsequently, they propose two non-overlapping DDFV Schwarz algorithms. DDFV discretizations are constructed with suitable transmission conditions. When using standard convection fluxes in the domain decomposition method, the iterative process converges to a system with modified fluxes at the interface. However, it is possible to modify the fluxes of the domain decomposition algorithm so that it converges to the reference scheme on the entire domain. Some numerical tests are presented to illustrate the behavior and the performances of the algorithms
Reviewer: Abdallah Bradji (Annaba)Strong bounded variation estimates for the multi-dimensional finite volume approximation of scalar conservation laws and application to a tumour growth modelhttps://zbmath.org/1491.650822022-09-13T20:28:31.338867Z"Remesan, Gopikrishnan Chirappurathu"https://zbmath.org/authors/?q=ai:remesan.gopikrishnan-chirappurathuThe author considers the finite volume approximation, on nonuniform Cartesian grids, of the nonlinear scalar conservation law \(\partial_t \alpha +\operatorname{div}(u f(\alpha )) = 0\) in two and three spatial dimensions with an initial data of bounded variation. A uniform estimate on total variation of discrete solutions is proved. The standard assumption which states that the advecting velocity vector is divergence free is relaxed. Since the underlying meshes are nonuniform Cartesian, it is possible to adaptively refine the mesh on regions where the solution is expected to have sharp fronts. A uniform BV estimate is also obtained for finite volume approximations of conservation laws that has a fully nonlinear flux on nonuniform Cartesian grids. Some numerical tests are presented to support the theoretical results.
Reviewer: Abdallah Bradji (Annaba)Fully-discrete finite element numerical scheme with decoupling structure and energy stability for the Cahn-Hilliard phase-field model of two-phase incompressible flow system with variable density and viscosityhttps://zbmath.org/1491.650912022-09-13T20:28:31.338867Z"Chen, Chuanjun"https://zbmath.org/authors/?q=ai:chen.chuanjun"Yang, Xiaofeng"https://zbmath.org/authors/?q=ai:yang.xiaofengSummary: We construct a fully-discrete finite element numerical scheme for the Cahn-Hilliard phase-field model of the two-phase incompressible flow system with variable density and viscosity. The scheme is linear, decoupled, and unconditionally energy stable. Its key idea is to combine the penalty method of the Navier-Stokes equations with the Strang operator splitting method, and introduce several nonlocal variables and their ordinary differential equations to process coupled nonlinear terms. The scheme is highly efficient and it only needs to solve a series of completely independent linear elliptic equations at each time step, in which the Cahn-Hilliard equation and the pressure Poisson equation only have constant coefficients. We rigorously prove the unconditional energy stability and solvability of the scheme and carry out numerous accuracy/stability examples and various benchmark numerical simulations in 2D and 3D, including the Rayleigh-Taylor instability and rising/coalescence dynamics of bubbles to demonstrate the effectiveness of the scheme, numerically.Analysis of fully discrete mixed finite element methods for time-dependent stochastic Stokes equations with multiplicative noisehttps://zbmath.org/1491.650922022-09-13T20:28:31.338867Z"Feng, Xiaobing"https://zbmath.org/authors/?q=ai:feng.xiaobing"Qiu, Hailong"https://zbmath.org/authors/?q=ai:qiu.hailongSummary: This paper is concerned with fully discrete mixed finite element approximations of the time-dependent stochastic Stokes equations with multiplicative noise. A prototypical method, which comprises of the Euler-Maruyama scheme for time discretization and the Taylor-Hood mixed element for spatial discretization is studied in detail. Strong convergence with rates is established not only for the velocity approximation but also for the pressure approximation (in a time-averaged fashion). A stochastic inf-sup condition is established and used in a nonstandard way to obtain the error estimate for the pressure approximation in the time-averaged fashion. Numerical results are also provided to validate the theoretical results and to gauge the performance of the proposed fully discrete mixed finite element methods.Local transparent boundary conditions for wave propagation in fractal trees. I: Method and numerical implementationhttps://zbmath.org/1491.650952022-09-13T20:28:31.338867Z"Joly, Patrick"https://zbmath.org/authors/?q=ai:joly.patrick"Kachanovska, Maryna"https://zbmath.org/authors/?q=ai:kachanovska.marynaA nonsymmetric approach and a quasi-optimal and robust discretization for the Biot's modelhttps://zbmath.org/1491.650962022-09-13T20:28:31.338867Z"Khan, Arbaz"https://zbmath.org/authors/?q=ai:khan.arbaz"Zanotti, Pietro"https://zbmath.org/authors/?q=ai:zanotti.pietroThe paper analyzes the numerical method for Biot's model describing the elastic wave propagation inside a porous medium saturated with a fluid. Variables in this model represent the displacement of the medium and the fluid pressure. In addition, there are several material parameters. However, spurious oscillations or volumetric locking may occur for specific values of these parameters. The authors focus on overcoming this problem and propose a method that is robust in the sense that it is uniformly stable with respect to all parameters.
First, the authors establish a novel nonsymmetric variational setting, where the norm measuring the data is not dual to the norm for measuring the solution. Then, they show the well-posedness of the setting and derive stability estimates. Furthermore, the authors propose a method that uses the backward Euler scheme for temporal discretization combined with the finite element method using first-order nonconforming Crouzeix-Raviart elements for the displacement and first-order discontinuous piecewise affine functions for the fluid pressure. The presented analysis of stability and error estimates leads to the conclusion that the method is robust and quasi-optimal. Finally, possible generalizations of the results are discussed.
Reviewer: Dana Černá (Liberec)Second-order convergence of the linearly extrapolated Crank-Nicolson method for the Navier-Stokes equations with \(H^1\) initial datahttps://zbmath.org/1491.650972022-09-13T20:28:31.338867Z"Li, Buyang"https://zbmath.org/authors/?q=ai:li.buyang"Ma, Shu"https://zbmath.org/authors/?q=ai:ma.shu"Wang, Na"https://zbmath.org/authors/?q=ai:wang.naSummary: This article concerns the numerical approximation of the two-dimensional nonstationary Navier-Stokes equations with \(H^1\) initial data. By utilizing special locally refined temporal stepsizes, we prove that the linearly extrapolated Crank-Nicolson scheme, with the usual stabilized Taylor-Hood finite element method in space, can achieve second-order convergence in time and space. Numerical examples are provided to support the theoretical analysis.Local and parallel efficient BDF2 and BDF3 rotational pressure-correction schemes for a coupled Stokes/Darcy systemhttps://zbmath.org/1491.650982022-09-13T20:28:31.338867Z"Li, Jian"https://zbmath.org/authors/?q=ai:li.jian.1"Wang, Xue"https://zbmath.org/authors/?q=ai:wang.xue"Al Mahbub, Md. Abdullah"https://zbmath.org/authors/?q=ai:al-mahbub.md-abdullah"Zheng, Haibiao"https://zbmath.org/authors/?q=ai:zheng.haibiao"Chen, Zhangxin"https://zbmath.org/authors/?q=ai:chen.zhangxinThis paper extends authors earlier work [\textit{J. Li} et al., Comput. Math. with Appl. 79, 337--353 (2020; Zbl 1443.65187); Numer. Methods Partial Differential Equations 35, 1873--1889 (2019; Zbl 1423.76253)] where first- and second-order (in time) BE (backward Euler) and BDF2 schemes with the rotational pressure-correction methods introduced in [\textit{J. Guermond} et al., SIAM J. Numer. Anal. 43, 239--258 (2005; Zbl 1083.76044)] are studied for a coupled Stokes/Darcy system. These temporal schemes are developed, and the BDF2/BDF3 rotational pressure-correction methods are studied for the Stokes/Darcy system. It was proven that the BDF2/BDF3 rotational pressure-correction methods are unconditionally stable, long-time accurate with a uniform-in-time error bound, and efficient in that only two decoupled equations are required to solve at each time step. At each time step, only one linear system of equations has to be solved, which thus significantly reduces the computational time and memory costs in practice. The presented projection methods are combined with the local and parallel methods based on full overlapping decoupled techniques for the coupled Stokes/Darcy system which increases the computational efficiency further. Several numerical examples are presented to illustrate the accuracy and efficiency of the proposed methods.
Reviewer: Bülent Karasözen (Ankara)A discontinuous Galerkin pressure correction scheme for the incompressible Navier-Stokes equations: stability and convergencehttps://zbmath.org/1491.650992022-09-13T20:28:31.338867Z"Masri, Rami"https://zbmath.org/authors/?q=ai:masri.rami"Liu, Chen"https://zbmath.org/authors/?q=ai:liu.chen"Riviere, Beatrice"https://zbmath.org/authors/?q=ai:riviere.beatrice-mSummary: A discontinuous Galerkin pressure correction numerical method for solving the incompressible Navier-Stokes equations is formulated and analyzed. We prove unconditional stability of the proposed scheme. Convergence of the discrete velocity is established by deriving a priori error estimates. Numerical results verify the convergence rates.New analysis and recovery technique of mixed FEMs for compressible miscible displacement in porous mediahttps://zbmath.org/1491.651012022-09-13T20:28:31.338867Z"Sun, Weiwei"https://zbmath.org/authors/?q=ai:sun.weiweiSummary: Numerical methods and analysis for compressible miscible flow in porous media have been investigated extensively in the last several decades. Amongst those methods, the lowest-order mixed method is the most popular one in practical applications. The method is based on the linear Lagrange approximation for the concentration and the lowest order (zero-order) Raviart-Thomas mixed approximation for the Darcy velocity/pressure. However, the existing error analysis only provides the first-order accuracy in \(L^2\)-norm for all three physical components in spatial direction, which was proved under certain extra restrictions on both time step and spatial meshes. The analysis is not optimal for the concentration mainly due to the strong coupling of the system and the drawback of the traditional approach which leads to serious pollution to the numerical concentration in analysis. The main task of this paper is to present a new analysis and establish the optimal error estimate of the commonly-used linearized lowest-order mixed FEM. In particular, the second-order accuracy for the concentration in spatial direction is proved unconditionally. Moreover, we propose a simple recovery technique to obtain a new numerical Darcy velocity/pressure of second-order accuracy by re-solving an elliptic pressure equation. Also we extend our analysis to a second-order time discrete scheme to obtain optimal error estimates in both spatial and temporal directions. Numerical results are provided to confirm our theoretical analysis and show the efficiency of the method.A two-grid combined mixed finite element and discontinuous Galerkin method for an incompressible miscible displacement problem in porous mediahttps://zbmath.org/1491.651042022-09-13T20:28:31.338867Z"Yang, Jiming"https://zbmath.org/authors/?q=ai:yang.jiming"Su, Yifan"https://zbmath.org/authors/?q=ai:su.yifanSummary: An incompressible miscible displacement problem is investigated. A two-grid algorithm of a full-discretized combined mixed finite element and discontinuous Galerkin approximation to the miscible displacement in porous media is proposed. The error estimate for the concentration in \(H^1\)-norm and the error estimates for the pressure and the velocity in \(L^2\)-norm are obtained. The analysis shows that the asymptotically optimal approximation can be achieved as long as the mesh size satisfies \(h = O(H^2)\), where \(H\) and \(h\) are the sizes of the coarse mesh and the fine mesh, respectively. Meanwhile, the effectiveness of the presented algorithm is verified by numerical experiments, from which it can be seen that the algorithm is spent much less time.Fully-discrete, decoupled, second-order time-accurate and energy stable finite element numerical scheme of the Cahn-Hilliard binary surfactant model confined in the Hele-Shaw cellhttps://zbmath.org/1491.651052022-09-13T20:28:31.338867Z"Yang, Xiaofeng"https://zbmath.org/authors/?q=ai:yang.xiaofengSummary: We consider the numerical approximation of the binary fluid surfactant phase-field model confined in a Hele-Shaw cell, where the system includes two coupled Cahn-Hilliard equations and Darcy equations. We develop a fully-discrete finite element scheme with some desired characteristics, including linearity, second-order time accuracy, decoupling structure, and unconditional energy stability. The scheme is constructed by combining the projection method for the Darcy equation, the quadratization approach for the nonlinear energy potential, and a decoupling method of using a trivial ODE built upon the ``zero-energy-contribution'' feature. The advantage of this scheme is that not only can all variables be calculated in a decoupled manner, but each equation has only constant coefficients at each time step. We strictly prove that the scheme satisfies the unconditional energy stability and give a detailed implementation process. Various numerical examples are further carried out to prove the effectiveness of the scheme, in which the benchmark Saffman-Taylor fingering instability problems in various flow regimes are simulated to verify the weakening effects of surfactant on surface tension.The convergence analysis of semi- and fully-discrete projection-decoupling schemes for the generalized Newtonian modelshttps://zbmath.org/1491.651072022-09-13T20:28:31.338867Z"Zhou, Guanyu"https://zbmath.org/authors/?q=ai:zhou.guanyuSummary: We propose two linear schemes (1st- and 2nd-order) for the generalized Newtonian flow with the shear-dependent viscosity, which combine the decoupling techniques with the projection methods. The linear stabilization terms mimic \(-k\partial_t \Delta{\boldsymbol{u}}\) and \(-k\partial_{tt} \Delta{\boldsymbol{u}}\) from the PDE point of view. By our schemes, each velocity component can be computed in parallel efficiently using the same solver \((I-\alpha^{-1}k\Delta)^{-1}\) at every time level. We analyze the convergence rates of the (temporally) semi- and the fully-discrete schemes. The theoretical results are testified by the numerical experiments.An efficient DWR-type a posteriori error bound of SDFEM for singularly perturbed convection-diffusion PDEshttps://zbmath.org/1491.651232022-09-13T20:28:31.338867Z"Avijit, D."https://zbmath.org/authors/?q=ai:avijit.d"Natesan, S."https://zbmath.org/authors/?q=ai:natesan.srinivasanSummary: This article deals with the residual-based a posteriori error estimation in the standard energy norm for the streamline-diffusion finite element method (SDFEM) for singularly perturbed convection-diffusion equations. The well-known dual-weighted residual (DWR) technique has been adopted to elevate the accuracy of the error estimator. Our main contribution is finding an efficient computable DWR-type robust residual-based a posteriori error bound for the SDFEM. The local lower error bound has also been provided. An adaptive mesh refinement algorithm has been addressed and lastly, some numerical experiments are carried out to justify the theoretical proofs.Two mixed finite element formulations for the weak imposition of the Neumann boundary conditions for the Darcy flowhttps://zbmath.org/1491.651262022-09-13T20:28:31.338867Z"Burman, Erik"https://zbmath.org/authors/?q=ai:burman.erik"Puppi, Riccardo"https://zbmath.org/authors/?q=ai:puppi.riccardoSummary: We propose two different discrete formulations for the weak imposition of the Neumann boundary conditions of the Darcy flow. The Raviart-Thomas mixed finite element on both triangular and quadrilateral meshes is considered for both methods. One is a consistent discretization depending on a weighting parameter scaling as \(\mathcal{O} (h^{-1})\), while the other is a penalty-type formulation obtained as the discretization of a perturbation of the original problem and relies on a parameter scaling as \(\mathcal{O} (h^{- k -1})\), \(k\) being the order of the Raviart-Thomas space. We rigorously prove that both methods are stable and result in optimal convergent numerical schemes with respect to appropriate mesh-dependent norms, although the chosen norms do not scale as the usual \(L^2\)-norm. However, we are still able to recover the optimal a priori \(L^2\)-error estimates for the velocity field, respectively, for high-order and the lowest-order Raviart-Thomas discretizations, for the first and second numerical schemes. Finally, some numerical examples validating the theory are exhibited.A fully-mixed formulation in Banach spaces for the coupling of the steady Brinkman-Forchheimer and double-diffusion equationshttps://zbmath.org/1491.651292022-09-13T20:28:31.338867Z"Caucao, Sergio"https://zbmath.org/authors/?q=ai:caucao.sergio"Gatica, Gabriel N."https://zbmath.org/authors/?q=ai:gatica.gabriel-n"Ortega, Juan P."https://zbmath.org/authors/?q=ai:ortega.juan-pabloSummary: We propose and analyze a new mixed finite element method for the nonlinear problem given by the coupling of the steady Brinkman-Forchheimer and double-diffusion equations. Besides the velocity, temperature, and concentration, our approach introduces the velocity gradient, the pseudostress tensor, and a pair of vectors involving the temperature/concentration, its gradient and the velocity, as further unknowns. As a consequence, we obtain a fully mixed variational formulation presenting a Banach spaces framework in each set of equations. In this way, and differently from the techniques previously developed for this and related coupled problems, no augmentation procedure needs to be incorporated now into the formulation nor into the solvability analysis. The resulting non-augmented scheme is then written equivalently as a fixed-point equation, so that the well-known Banach theorem, combined with classical results on nonlinear monotone operators and Babuška-Brezzi's theory in Banach spaces, are applied to prove the unique solvability of the continuous and discrete systems. Appropriate finite element subspaces satisfying the required discrete inf-sup conditions are specified, and optimal \textit{a priori} error estimates are derived. Several numerical examples confirm the theoretical rates of convergence and illustrate the performance and flexibility of the method.Analysis of a stabilized finite element approximation for a linearized logarithmic reformulation of the viscoelastic flow problemhttps://zbmath.org/1491.651302022-09-13T20:28:31.338867Z"Codina, Ramon"https://zbmath.org/authors/?q=ai:codina.ramon"Moreno, Laura"https://zbmath.org/authors/?q=ai:moreno.lauraSummary: In this paper we present the numerical analysis of a finite element method for a linearized viscoelastic flow problem. In particular, we analyze a linearization of the logarithmic reformulation of the problem, which in particular should be able to produce results for Weissenberg numbers higher than the standard one. In order to be able to use the same interpolation for all the unknowns (velocity, pressure and logarithm of the conformation tensor), we employ a stabilized finite element formulation based on the Variational Multi-Scale concept. The study of the linearized problem already serves to show why the logarithmic reformulation performs better than the standard one for high Weissenberg numbers; this is reflected in the stability and error estimates that we provide in this paper.An embedded discontinuous Galerkin method for the Oseen equationshttps://zbmath.org/1491.651372022-09-13T20:28:31.338867Z"Han, Yongbin"https://zbmath.org/authors/?q=ai:han.yongbin"Hou, Yanren"https://zbmath.org/authors/?q=ai:hou.yanrenSummary: In this paper, the \textit{a priori} error estimates of an embedded discontinuous Galerkin method for the Oseen equations are presented. It is proved that the velocity error in the \(L^2 (\Omega)\) norm, has an optimal error bound with convergence order \(k+1\), where the constants are dependent on the Reynolds number (or \(\nu^{-1})\), in the diffusion-dominated regime, and in the convection-dominated regime, it has a Reynolds-robust error bound with quasi-optimal convergence order \(k+1/2\). Here, \(k\) is the polynomial order of the velocity space. In addition, we also prove an optimal error estimate for the pressure. Finally, we carry out some numerical experiments to corroborate our analytical results.Numerical upscaling for heterogeneous materials in fractured domainshttps://zbmath.org/1491.651382022-09-13T20:28:31.338867Z"Hellman, Fredrik"https://zbmath.org/authors/?q=ai:hellman.fredrik"Målqvist, Axel"https://zbmath.org/authors/?q=ai:malqvist.axel"Wang, Siyang"https://zbmath.org/authors/?q=ai:wang.siyangSummary: We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise \textit{e.g.} in fractured porous media, reinforced materials, and electric circuits. The main computational challenge is the high resolution needed to resolve the data variation. We propose a multiscale method that models the thin structures as interfaces and incorporate heterogeneities in corrected shape functions. The construction results in an accurate upscaled representation of the system that can be used to solve for several forcing functions or to simulate evolution problems in an efficient way. By introducing a novel interpolation operator, defining the fine scale of the problem, we prove exponential decay of the shape functions which allows for a sparse approximation of the upscaled representation. An \textit{a priori} error bound is also derived for the proposed method together with numerical examples that verify the theoretical findings. Finally we present a numerical example to show how the technique can be applied to evolution problems.A stabilized nonconforming Nitsche's extended finite element method for Stokes interface problemshttps://zbmath.org/1491.651402022-09-13T20:28:31.338867Z"He, Xiaoxiao"https://zbmath.org/authors/?q=ai:he.xiaoxiao"Song, Fei"https://zbmath.org/authors/?q=ai:song.fei"Deng, Weibing"https://zbmath.org/authors/?q=ai:deng.weibingThe paper deals with the numerical solution of the Stokes interface problem by a stabilized extended finite element method on unfitted triangulation elements which do not require the interface align with the triangulation. The problem is written on mixed form using nonconforming \(P_1\) velocity and elementwise \(P_0\) pressure. Extra stabilization terms involving velocity and pressure are added in the discrete bilinear form. An inf-sup stability result is derived, which is uniform with respect to mesh size \(h\), the viscosity and the position of the interface. An optimal priori error estimates are obtained. Moreover, the errors in energy norm for velocity and in \(L_2\) norm for pressure are uniform to the viscosity and the location of the interface. Two numerical examples are presented to support the theoretical analysis.
Reviewer: Vit Dolejsi (Praha)Error analysis of higher order trace finite element methods for the surface Stokes equationhttps://zbmath.org/1491.651422022-09-13T20:28:31.338867Z"Jankuhn, Thomas"https://zbmath.org/authors/?q=ai:jankuhn.thomas"Olshanskii, Maxim A."https://zbmath.org/authors/?q=ai:olshanskii.maxim-a"Reusken, Arnold"https://zbmath.org/authors/?q=ai:reusken.arnold"Zhiliakov, Alexander"https://zbmath.org/authors/?q=ai:zhiliakov.alexanderSummary: The paper studies a higher order unfitted finite element method for the Stokes system posed on a surface in \(\mathbb{R}^3\). The method employs parametric \(\mathbf{P}_k\)-\(P_{k-1}\) finite element pairs on tetrahedral bulk mesh to discretize the Stokes system on embedded surface. Stability and optimal order convergence results are proved. The proofs include a complete quantification of geometric errors stemming from approximate parametric representation of the surface. Numerical experiments include formal convergence studies and an example of the Kelvin-Helmholtz instability problem on the unit sphere.Coupled iterative analysis for stationary inductionless magnetohydrodynamic system based on charge-conservative finite element methodhttps://zbmath.org/1491.651542022-09-13T20:28:31.338867Z"Zhang, Xiaodi"https://zbmath.org/authors/?q=ai:zhang.xiaodi"Ding, Qianqian"https://zbmath.org/authors/?q=ai:ding.qianqianSummary: This paper considers charge-conservative finite element approximation and three coupled iterations of stationary inductionless magnetohydrodynamics equations in Lipschitz domain. Using a mixed finite element method, we discretize the hydrodynamic unknowns by stable velocity-pressure finite element pairs, discretize the current density and electric potential by \(\boldsymbol{H}(\operatorname{div},\varOmega)\times L^2(\varOmega)\)-comforming finite element pairs. The well-posedness of this formula and the optimal error estimate are provided. In particular, we show that the error estimates for the velocity, the current density and the pressure are independent of the electric potential. With this, we propose three coupled iterative methods: Stokes, Newton and Oseen iterations. Rigorous analysis of convergence and stability for different iterative schemes are provided, in which we improve the stability conditions for both Stokes and Newton iterative method. Numerical results verify the theoretical analysis and show the applicability and effectiveness of the proposed methods.Port-Hamiltonian formulations of poroelastic network modelshttps://zbmath.org/1491.740202022-09-13T20:28:31.338867Z"Altmann, R."https://zbmath.org/authors/?q=ai:altmann.robert"Mehrmann, V."https://zbmath.org/authors/?q=ai:mehrmann.volker-ludwig"Unger, B."https://zbmath.org/authors/?q=ai:unger.brian-w|unger.benjaminSummary: We investigate an energy-based formulation of the two-field poroelasticity model and the related multiple-network model as they appear in geosciences or medical applications. We propose a port-Hamiltonian formulation of the system equations, which is beneficial for preserving important system properties after discretization or model-order reduction. For this, we include the commonly omitted second-order term and consider the corresponding first-order formulation. The port-Hamiltonian formulation of the quasi-static case is then obtained by (formally) setting the second-order term zero. Further, we interpret the poroelastic equations as an interconnection of a network of submodels with internal energies, adding a control-theoretic understanding of the poroelastic equations.Fluid-structure coupling simulation of explosive flow field in heterogeneous porous media based on fractal theoryhttps://zbmath.org/1491.740232022-09-13T20:28:31.338867Z"Zhu, Qingyong"https://zbmath.org/authors/?q=ai:zhu.qingyong"Lu, Shun"https://zbmath.org/authors/?q=ai:lu.shun"Lai, Dongheng"https://zbmath.org/authors/?q=ai:lai.dongheng"Sun, Junjun"https://zbmath.org/authors/?q=ai:sun.junjunDispersion of waves in two and three-dimensional periodic mediahttps://zbmath.org/1491.740572022-09-13T20:28:31.338867Z"Godin, Yuri A."https://zbmath.org/authors/?q=ai:godin.yuri-a"Vainberg, Boris"https://zbmath.org/authors/?q=ai:vainberg.boris-rSummary: We consider the propagation of acoustic time-harmonic waves in homogeneous media containing periodic lattices of spherical or cylindrical inclusions. It is assumed that the wavelength has the order of the periods of the lattice while the radius \(a\) of inclusions is small. A new approach is suggested to derive the complete asymptotic expansions of the dispersion relations in two- and three-dimensional cases as \(a\to0\) and first several terms of the expansions are evaluated explicitly. Our method is based on the reduction of the original singularly perturbed (by inclusions) problem to the regular one. The Dirichlet, Neumann, and transmission boundary conditions are considered. In the former case, we estimate the cutoff wavelength \(\lambda_{\mathrm{max}}\) supported by the periodic medium in two and three dimensions. The effective wave speed is obtained as a function of the wave frequency, the filling fraction of the inclusions, and the physical properties of the constituents of the mixture. Dependence of the asymptotic formulas obtained in the paper on geometric and material parameters is illustrated by graphs.Open-channel flowhttps://zbmath.org/1491.760012022-09-13T20:28:31.338867Z"Chaudhry, M. Hanif"https://zbmath.org/authors/?q=ai:chaudhry.m-hanifPublisher's description: Now in the third edition, this text on open-channel flow presents introductory material on the topic as well as up-to-date information for the planning, design, and operation of water-resource projects. It has a very strong emphasis on the application of efficient solution techniques, computational procedures, and modern methods of analysis and provides detailed coverage of steady and unsteady flows. The new edition includes a new chapter on the modeling of levee breach, new sections on hydraulic models and velocity measurements, new and updated references and problem sets and exercises, and a solutions manual. The material has been class tested over many years and the book is an ideal textbook for students in senior-level undergraduate and graduate courses on open-channel flow and hydraulic engineering, and as a reference for civil engineers needing up-to-date information on the latest developments in open-channel flow.
\begin{itemize}
\item
Detailed coverage of steady and unsteady flows;
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Includes practical examples and sample computer programs in Python;
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New problem sets, some designed especially for take-home tests, and a solution manual for instructors.
\end{itemize}
See the review of the 2nd edition in [Zbl 1149.76001]. For the 1st edition see [Zbl 1138.76002].Internal waves in the ocean. Theory and practicehttps://zbmath.org/1491.760022022-09-13T20:28:31.338867Z"Stastna, Marek"https://zbmath.org/authors/?q=ai:stastna.marekPublisher's description: This monograph provides a concise overview of nonlinear internal wave theory. It serves as a self-contained reference for both students of mathematics as well as scientific professionals by presenting the material in two parts, isolating the narrative analysis from the mathematical detail. This unique format allows the text to remain accessible to oceanographers and researchers outside of mathematics by presenting a range of relevant theories on their own terms. Conversely, it enables applied mathematicians to understand how the conversation between mathematics and sciences proceeds in a field that has developed through a combination of the two. In addition, the text is supplemented by hands-on Matlab software, as the book incorporates a collection of working codes that enable readers to reproduce all theoretical figures in the text, with modification potential to fit a range of applications including a number of mini-projects outlined throughout the text.Designing complex fluidshttps://zbmath.org/1491.760032022-09-13T20:28:31.338867Z"Ewoldt, Randy H."https://zbmath.org/authors/?q=ai:ewoldt.randy-h"Saengow, Chaimongkol"https://zbmath.org/authors/?q=ai:saengow.chaimongkolSummary: Taking a small step away from Newtonian fluid behavior creates an explosion in the range of possibilities. Non-Newtonian fluid properties can achieve diverse flow objectives, but the complexity introduces challenges. We survey useful rheological complexity along with organizing principles and design methods as we consider the following questions: How can non-Newtonian properties be useful? What properties are needed? How can we get those properties?
For the entire collection see [Zbl 1489.76002].Entropy generation in Casson nanofluid flow past an electromagnetic stretching Riga platehttps://zbmath.org/1491.760042022-09-13T20:28:31.338867Z"Oyelakin, I. S."https://zbmath.org/authors/?q=ai:oyelakin.i-s"Ghosh, R."https://zbmath.org/authors/?q=ai:ghosh.riya"Mondal, S."https://zbmath.org/authors/?q=ai:mondal.sabyasachi"Sibanda, P."https://zbmath.org/authors/?q=ai:sibanda.preciousSummary: This paper investigates entropy generation in a Casson nanofluid flow past an electromagnetic stretching Riga plate. Entropy generation is a measure of irreversibility factors in thermodynamic processes. It is a common feature in heat transfer studies, and as such, the study includes the effect of viscous dissipation. We solve the model equations using the spectral local linearization method. The study considers the impact of some other physical parameters like the Casson, velocity ratio, and electromagnetic parameters. A good correlation is achieved when the present results are compared with published literature. The results indicate that the velocity ratio parameter significantly influences the fluid flow, temperature, and concentration profiles. The entropy generation increases with an increase in concentration and Brinkmann number, whereas an opposite behavior is observed for increasing the value of the modified Hartmann number. Again, increasing the Casson parameter increases the temperature and concentration profiles, whereas the velocity profile reduces.Computational investigation of Stefan blowing effect on flow of second-grade fluid over a curved stretching sheethttps://zbmath.org/1491.760052022-09-13T20:28:31.338867Z"Punith Gowda, R. J."https://zbmath.org/authors/?q=ai:gowda.r-j-punith"Baskonus, Haci Mehmet"https://zbmath.org/authors/?q=ai:baskonus.haci-mehmet"Naveen Kumar, R."https://zbmath.org/authors/?q=ai:kumar.r-naveen"Prasannakumara, B. C."https://zbmath.org/authors/?q=ai:prasannakumara.b-c"Prakasha, D. G."https://zbmath.org/authors/?q=ai:prakasha.doddabhadrappla-gowdaSummary: Non-Newtonian fluids have extensive range of applications in the field of industries like plastics processing, manufacturing of electronic devices, lubrication flows, medicine and medical equipment. Stimulated from these applications, a theoretical analysis is carried out to scrutinize the flow of a second-grade liquid over a curved stretching sheet with the impact of Stefan blowing condition, thermophoresis and Brownian motion. The modelled governing equations for momentum, thermal and concentration are deduced to a system of ordinary differential equations by introducing suitable similarity transformations. These reduced equations are solved using Runge-Kutta-Fehlberg fourth fifth order method (RKF-45) by adopting shooting technique. The solutions for the flow, heat and mass transference features are found numerically and presented with the help of graphical illustrations. Results reveal that, curvature and Stefan blowing parameters have propensity to rise the heat transfer. Further, second grade fluid shows high rate of mass and heat transfer features when related to Newtonian fluid for upsurge in values of Brownian motion parameter.Global well posedness for a Q-tensor model of nematic liquid crystalshttps://zbmath.org/1491.760062022-09-13T20:28:31.338867Z"Murata, Miho"https://zbmath.org/authors/?q=ai:murata.miho"Shibata, Yoshihiro"https://zbmath.org/authors/?q=ai:shibata.yoshihiroSummary: In this paper, we prove the global well posedness and the decay estimates for a \(\mathbb{Q}\)-tensor model of nematic liquid crystals in \(\mathbb{R}^N\), \(N \ge 3\). This system is a coupled system by the Navier-Stokes equations with a parabolic-type equation describing the evolution of the director fields \(\mathbb{Q}\). The proof is based on the maximal \(L_p\)-\(L_q\) regularity and the \(L_p\)-\(L_q\) decay estimates to the linearized problem.Retraction of thin films coated by insoluble surfactantshttps://zbmath.org/1491.760072022-09-13T20:28:31.338867Z"De Corato, Marco"https://zbmath.org/authors/?q=ai:de-corato.marco"Tammaro, Daniele"https://zbmath.org/authors/?q=ai:tammaro.daniele"Maffettone, Pier Luca"https://zbmath.org/authors/?q=ai:maffettone.pier-luca"Fueyo, Norberto"https://zbmath.org/authors/?q=ai:fueyo.norbertoSummary: We investigate the retraction of a circular thin film coated with insoluble surfactants, which is punctured at its centre. We assume that the surface pressure of the liquid-gas interface is related to the number density of surfactants through a linear equation of state, which is characterized by a single parameter: the Gibbs dilation modulus. To solve the governing equations and track the deformation of the domain, we use the finite element method with an arbitrary Lagrangian-Eulerian approach where the film surface is sharp. Our simulations show that the surface elasticity introduced by the surfactants slows down the retraction and introduces oscillations at early times. In agreement with previous experiments and theoretical analysis, we find that the presence of surfactants introduces perturbations of the film thickness over progressively larger distances as the surface elasticity increases. The surface perturbations travel faster than the retracting edge of the film at a speed proportional to the Gibbs modulus. For large values of the Gibbs modulus, the interface behaviour approaches that of an incompressible two-dimensional solid. Our analysis sheds light on the effect of insoluble surfactants on the opening of a circular hole in a thin film and can be extended to investigate the onset of surface cracks and fractures.Multiscale modelling and splitting approaches for fluids composed of Coulomb-interacting particleshttps://zbmath.org/1491.760082022-09-13T20:28:31.338867Z"Geiser, Jürgen"https://zbmath.org/authors/?q=ai:geiser.jurgenSummary: We consider fluids composed of Coulomb-interacting particles, which are modelled by the Fokker-Planck equation with a collision operator. Based on modelling the transport and collision of the particles, we propose new, computationally efficient, algorithms based on splitting the equations of motion into a global Newtonian transport equation, where the effects of an external electric field are considered, and a local Coulomb interaction stochastic differential equation, which determines the new velocities of the particle. Two different numerical schemes, one deterministic and the other stochastic, as well as an Hamiltonian splitting approach, are proposed for coupling the interactionand transport equations. Results are presented for two- and multi-particle systems with different approximations for the Coulomb interaction. Methodologically, the transport part is modelled by the kinetic equations and the collision part is modelled by the Langevin equations with Coulomb collisions. Such splitting approaches allow concentrating on different solver methods for each different part. Further, we solve multiscale problems involving an external electrostatic field. We apply a multiscale approach so that we can decompose the different time-scales of the transport and the collision parts. We discuss the benefits of the different splitting approaches and their numerical analysis.Comparison of two higher accuracy unstructured scale-resolving approaches applied to dual-stream nozzle jet simulationhttps://zbmath.org/1491.760092022-09-13T20:28:31.338867Z"Bosnyakov, S. M."https://zbmath.org/authors/?q=ai:bosnyakov.s-m"Volkov, A. V."https://zbmath.org/authors/?q=ai:volkov.alexander-v|volkov.aleksei-vasilevich"Duben', A. P."https://zbmath.org/authors/?q=ai:duben.a-p"Zapryagaev, V. I."https://zbmath.org/authors/?q=ai:zapryagaev.v-i"Kozubskaya, T. K."https://zbmath.org/authors/?q=ai:kozubskaya.tatiana-k"Mikhaĭlov, S. V."https://zbmath.org/authors/?q=ai:mikhailov.s-v"Troshin, A. I."https://zbmath.org/authors/?q=ai:troshin.a-i"Tsvetkova, V. O."https://zbmath.org/authors/?q=ai:tsvetkova.v-oSummary: Dual-stream nozzle jet computations conducted using different numerical algorithms developed in TsAGI and KIAM RAS are presented. Scale-resolving approaches of DES family based on higher accuracy numerical methods are applied. The flow considered was studied experimentally at ITAM SB RAS. The jet was axisymmetric up to the influence of the supporting pylons, cold, subsonic at the inner nozzle exit and supersonic at the outer nozzle exit. The computational data is compared with the experiment and with each other.One-dimensional unsteady flow from a cylindrical draining tankhttps://zbmath.org/1491.760102022-09-13T20:28:31.338867Z"Marotta, Sebastian M."https://zbmath.org/authors/?q=ai:marotta.sebastian-m"Geeter, Chris"https://zbmath.org/authors/?q=ai:geeter.chris"Huynh, Richard"https://zbmath.org/authors/?q=ai:huynh.richardSummary: We study the differential equation that corresponds to the one-dimensional frictionless unsteady flow model of a cylindrical draining tank. We survey previous results, solve the equation applying new changes of variables and procedures, and present new exact elementary solutions. The problem provides an excellent example of application that is accessible to undergraduate students after a first course on differential equations.Flood inundation predictionhttps://zbmath.org/1491.760112022-09-13T20:28:31.338867Z"Bates, Paul D."https://zbmath.org/authors/?q=ai:bates.paul-dSummary: Every year flood events lead to thousands of casualties and significant economic damage. Mapping the areas at risk of flooding is critical to reducing these losses, yet until the last few years such information was available for only a handful of well-studied locations. This review surveys recent progress to address this fundamental issue through a novel combination of appropriate physics, efficient numerical algorithms, high-performance computing, new sources of big data, and model automation frameworks. The review describes the fluid mechanics of inundation and the models used to predict it, before going on to consider the developments that have led in the last five years to the creation of the first true fluid mechanics models of flooding over the entire terrestrial land surface.
For the entire collection see [Zbl 1489.76002].Wave breaking in undular bores with shear flowshttps://zbmath.org/1491.760122022-09-13T20:28:31.338867Z"Bjørnestad, Maria"https://zbmath.org/authors/?q=ai:bjornestad.maria"Kalisch, Henrik"https://zbmath.org/authors/?q=ai:kalisch.henrik"Abid, Malek"https://zbmath.org/authors/?q=ai:abid.malek"Kharif, Christian"https://zbmath.org/authors/?q=ai:kharif.christian"Brun, Mats"https://zbmath.org/authors/?q=ai:brun.mats-kirkesaetherSummary: It is well known that weak hydraulic jumps and bores develop a growing number of surface oscillations behind the bore front. Defining the bore strength as the ratio of the head of the undular bore to the undisturbed depth, it was found in the classic work of \textit{H. Favre} [Ondes de translation. Paris: Dunod (1935)] that the regime of laminar flow is demarcated from the regime of partially turbulent flows by a sharply defined value 0.281. This critical bore strength is characterized by the eventual breaking of the leading wave of the bore front. Compared to the flow depth in the wave flume, the waves developing behind the bore front are long and of small amplitude, and it can be shown that the situation can be described approximately using the well known Kortweg-de Vries equation. In the present contribution, it is shown that if a shear flow is incorporated into the KdV equation, and a kinematic breaking criterion is used to test whether the waves are spilling, then the critical bore strength can be found theoretically within an error of less than ten percent.Water-wave studies on a (2+1)-dimensional generalized variable-coefficient Boiti-Leon-Pempinelli systemhttps://zbmath.org/1491.760132022-09-13T20:28:31.338867Z"Gao, Xiao-Tian"https://zbmath.org/authors/?q=ai:gao.xiao-tian"Tian, Bo"https://zbmath.org/authors/?q=ai:tian.boSummary: Studies on the water waves are undertaken in hydrodynamics. In this Letter, a (2+1)-dimensional generalized variable-coefficient Boiti-Leon-Pempinelli system describing the water waves in an infinitely narrow channel of constant depth is taken into consideration. Through symbolic computation, concerning the horizontal velocity and elevation of the water wave, this Letter presents two branches of the similarity reductions.Symbolic computation on a \((2+1)\)-dimensional generalized variable-coefficient Boiti-Leon-Pempinelli system for the water waveshttps://zbmath.org/1491.760142022-09-13T20:28:31.338867Z"Gao, Xin-Yi"https://zbmath.org/authors/?q=ai:gao.xinyi"Guo, Yong-Jiang"https://zbmath.org/authors/?q=ai:guo.yongjiang"Shan, Wen-Rui"https://zbmath.org/authors/?q=ai:shan.wenruiSummary: Water waves attract people's attention. For the water waves, a \((2+1)\)-dimensional generalized variable-coefficient Boiti-Leon-Pempinelli system is hereby studied. As for the horizontal velocity and elevation of the water wave, on the one hand, with the scaling transformations and symbolic computation, a set of the hetero-Bäcklund transformations is constructed, linking the original system with a known generalized variable-coefficient Burgers equation. As for the horizontal velocity and elevation of the water wave, on the other hand, with symbolic computation, a set of the similarity reductions is constructed, from the original system to a known ordinary differential equation. All our results depend on the variable coefficients in the original system.Water wave scattering by a thin vertical submerged permeable platehttps://zbmath.org/1491.760152022-09-13T20:28:31.338867Z"Gayen, Rupanwita"https://zbmath.org/authors/?q=ai:gayen.rupanwita"Gupta, Sourav"https://zbmath.org/authors/?q=ai:gupta.sourav"Chakrabarti, Aloknath"https://zbmath.org/authors/?q=ai:chakrabarti.aloknathSummary: An alternative approach is proposed here to investigate the problem of scattering of surface water waves by a vertical permeable plate submerged in deep water within the framework of linear water wave theory. Using Havelock's expansion of water wave potential, the associated boundary value problem is reduced to a second kind hypersingular integral equation of order 2. The unknown function of the hypersingular integral equation is expressed as a product of a suitable weight function and an unknown polynomial. The associated hypersingular integral of order 2 is evaluated by representing it as the derivative of a singular integral of the Cauchy type which is computed by employing an idea explained in Gakhov's book [\textit{F. D. Gakhov}, Boundary value problems. Oxford-London-Edinburgh-New York-Paris-Frankfurt: Pergamon Press (1966; Zbl 0141.08001)]. The values of the reflection coefficient computed with the help of present method match exactly with the previous results available in the literature. The energy identity is derived using the Havelock's theorems.On the structure of steady parasitic gravity-capillary waves in the small surface tension limithttps://zbmath.org/1491.760162022-09-13T20:28:31.338867Z"Shelton, Josh"https://zbmath.org/authors/?q=ai:shelton.josh"Milewski, Paul"https://zbmath.org/authors/?q=ai:milewski.paul-a"Trinh, Philippe H."https://zbmath.org/authors/?q=ai:trinh.philippe-hSummary: When surface tension is included in the classical formulation of a steadily travelling gravity wave (a Stokes wave), it is possible to obtain solutions that exhibit parasitic ripples: small capillary waves riding on the surface of steep gravity waves. However, it is not clear whether the singular small surface tension limit is well posed. That is, is it possible for an appropriate travelling gravity-capillary wave to be continuously deformed to the classic Stokes wave in the limit of vanishing surface tension? The work of \textit{B. Chen} and \textit{P. G. Saffman} [Stud. Appl. Math. 62, 1--21 (1980; Zbl 0446.76023)] had suggested smooth continuation was not possible, while the numerical study of \textit{L. W. Schwartz} and \textit{J.-M. Vanden-Broeck} [J. Fluid Mech. 95, 119--139 (1979; Zbl 0419.76014)] used an amplitude parameter that made it difficult to understand the structure of solutions for small values of the surface tension. In this paper we numerically explore the low surface tension limit of the steep gravity-capillary travelling-wave problem. Our results allow for a classification of the bifurcation structure that arises, and serve to unify a number of previous numerical studies. Crucially, we demonstrate that different choices of solution amplitude can lead to subtle restrictions on the continuation procedure. When wave energy is used as a continuation parameter, solution branches can be continuously deformed to the zero surface tension limit of a travelling Stokes wave.Dynamics of nonlinear waves in a Burridge and Knopoff model for earthquake with long-range interactions, velocity-dependent and hydrodynamics friction forceshttps://zbmath.org/1491.760172022-09-13T20:28:31.338867Z"Nkomom, Théodule Nkoa"https://zbmath.org/authors/?q=ai:nkomom.theodule-nkoa"Ndzana, Fabien II"https://zbmath.org/authors/?q=ai:ndzana.fabien-ii"Okaly, Joseph Brizar"https://zbmath.org/authors/?q=ai:okaly.joseph-brizar"Mvogo, Alain"https://zbmath.org/authors/?q=ai:mvogo.alainSummary: We investigate the dynamics of nonlinear waves in a long-range extension of the Burridge and Knopoff model for earthquake. We consider the dissipative hydrodynamics forces. The spatio-temporal dynamics of the system is found by introducing in the coupling spring and hydrodynamics forces a linear term that decays as a power-law, with an exponent \(s\) such that \(1<s\leq 3\). The theoretical framework for the analysis is presented in the rotative wave approximation. Due to the non analytic properties of the dispersion relation, we use the discrete derivative operator technique. The dynamics of the system is governed by the complex Ginzburg-Landau equation, allowing breather-like soliton solutions. We use the relevant case \(s=2\), and results show that the magnitude, the velocity, and area of propagation of nonlinear waves strongly depend on the frictions forces. Our analytical results are in good agreement with numerical experiments and confirm the correctness of the method.Vortex collapses for the Euler and quasi-geostrophic modelshttps://zbmath.org/1491.760182022-09-13T20:28:31.338867Z"Godard-Cadillac, Ludovic"https://zbmath.org/authors/?q=ai:godard-cadillac.ludovicSummary: This article studies point-vortex models for the Euler and surface quasi-geostrophic equations. In the case of an inviscid fluid with planar motion, the point-vortex model gives account of dynamics where the vorticity profile is sharply concentrated around some points and approximated by Dirac masses. This article contains two main theorems and also smaller propositions with several links between each other. The first main result focuses on the Euler point-vortex model, and under the non-neutral cluster hypothesis we prove a convergence result. The second result is devoted to the generalization of a classical result by \textit{C. Marchioro} and \textit{M. Pulvirenti} [Mathematical theory of incompressible nonviscous fluids. New York, NY: Springer-Verlag (1994; Zbl 0789.76002)] concerning the improbability of collapses and the extension of this result to the quasi-geostrophic case.Laminar flow of a viscous liquid in the entrance region of a circular pipehttps://zbmath.org/1491.760192022-09-13T20:28:31.338867Z"Kazakov, L. I."https://zbmath.org/authors/?q=ai:kazakov.l-iSummary: An approximate theory of stationary axisymmetric laminar flow of a viscous incompressible fluid in the entrance region of a circular pipe is presented. It gives correct (within \(\pm 2\)\%) calculated values of different physical characteristics of the established flow, which coincide with the known calculated and experimental data. Instead of the traditional Bernoulli equation for the entire length of the entrance region, the work at hand uses the equation of the axial pressure gradient averaged over the pipe section to determine the pressure value.Navier-Stokes equations, the algebraic aspecthttps://zbmath.org/1491.760202022-09-13T20:28:31.338867Z"Zharinov, V. V."https://zbmath.org/authors/?q=ai:zharinov.victor-vSummary: We present an analysis of the Navier-Stokes equations in the framework of an algebraic approach to systems of partial differential equations (the formal theory of differential equations).\(L^p\)-strong solution for the stationary exterior Stokes equations with Navier boundary conditionhttps://zbmath.org/1491.760212022-09-13T20:28:31.338867Z"Dhifaoui, Anis"https://zbmath.org/authors/?q=ai:dhifaoui.anisLet \(\Omega \subset \mathbb{R}^3\) be an unbounded domain with compact boundary of class \(C^{2,1}\) such that \(\mathbb{R}^3\setminus \overline \Omega \) is connected. The paper studies the Stokes system with Navier boundary condition \( -\Delta u+\nabla p=f\), \( \nabla \cdot u=0 \) in \( \Omega \), \( u_n=g\), \( [T(u,p)n^\Omega +\alpha u]_\tau = h \) on \( \partial \Omega \). A solution \( (u,p)\) is from the weighted Sobolev spaces \( W^{2,q}_{k+1}(\Omega )\times W^{1,q}_{k+1}(\Omega )\).
Reviewer: Dagmar Medková (Praha)An alternative proof of \(L^q-L^r\) estimates of the Oseen semigroup in higher dimensional exterior domainshttps://zbmath.org/1491.760222022-09-13T20:28:31.338867Z"Hishida, Toshiaki"https://zbmath.org/authors/?q=ai:hishida.toshiakiSummary: \(L^q-L^r\) decay estimates of the Oseen semigroup in \(n\)-dimensional exterior domains were well established by \textit{T. Kobayashi} and \textit{Y. Shibata} [Math. Ann. 310, No. 1, 1--45 (1998; Zbl 0891.35114)] \((n=3)\), \textit{Y. Enomoto} and \textit{Y. Shibata} [J. Math. Fluid Mech. 7, No. 3, 339--367 (2005; Zbl 1094.35097)] \((n\ge 3)\) and \textit{Y. Maekawa} [J. Inst. Math. Jussieu 20, No. 3, 859--891 (2021; Zbl 1465.76032)] \((n=2)\). The same result has been recently proved by the present author [Math. Ann. 372, No. 3--4, 915--949 (2018; Zbl 1405.35139); Arch. Ration. Mech. Anal. 238, No. 1, 215--254 (2020; Zbl 1446.35100)] for a generalized Oseen evolution operator in 3-dimensional exterior domains, where rotation as well as translation of a rigid body is taken into account and, moreover, both translational and angular velocities can be time-dependent. The approach developed there can be considerably simplified if both the non-autonomous character and rotation are absent. As a consequence, an alternative short proof of decay estimates of the Oseen semigroup can be available without relying on analysis of the resolvent and the argument works for \(n\ge 3\) as well. I thus believe that the presentation of the proof would be worth publishing here.Variable viscosity effect on boundary layer flow along continuously moving plate with the thermal boundary condition of the third kindhttps://zbmath.org/1491.760232022-09-13T20:28:31.338867Z"Jha, Basant K."https://zbmath.org/authors/?q=ai:jha.basant-k"Samaila, Gabriel"https://zbmath.org/authors/?q=ai:samaila.gabrielSummary: An incompressible and viscous fluid flow past a constant moving plate with convective boundary condition considering the variable viscosity effect is fully presented. The solution to the governing equation is obtained by Runge Kutta Ferberg four-fifth order (RKF45) method in Maple software. Four fluids namely; mercury, air, sulphur oxide and water whose respective Prandtl numbers are 0.044, 0.72, 2 and 7 are considered during the computation. The effect of the controlling parameters such Biot number \((Bi)\), Prandtl number (Pr), reference temperature \(( \theta_r)\) and exponential constant (N) on the temperature distribution, velocity profile, Nusselt number and the Skin friction is presented using tables and line graphs. It is found that the temperature distribution is inversely proportional to Biot number \((Bi)\) augment whereas the velocity profile decreases as the reference temperature \(( \theta_r)\) propagates. The results also revealed that the thickness of the thermal boundary layer decrease as Prandtl number (Pr) increases. For liquids fluid, the skin friction increases with the exponential constant \((N)\) propagation whereas decreases for gases fluid. The effect of the Biot number on the skin friction exhibits opposite behaviour with that of the exponential constant. Regarding the Nusselt number, the exponential constant augment increases the Nusselt number for both gases and liquids fluid.Vortex reconnection and turbulence cascadehttps://zbmath.org/1491.760242022-09-13T20:28:31.338867Z"Yao, Jie"https://zbmath.org/authors/?q=ai:yao.jie"Hussain, Fazle"https://zbmath.org/authors/?q=ai:hussain.fazleSummary: As a fundamental topology-transforming event, reconnection plays a significant role in the dynamics of plasmas, polymers, DNA, and fluids -- both (classical) viscous and quantum. Since the 1994 review by \textit{S. Kida} and \textit{M. Takaoka} [Annu. Rev. Fluid Mech. 26, 169--189 (1994; Zbl 0802.76016)], substantial advances have been made on this topic. We review recent studies of vortex reconnection in (classical) viscous flows, including the physical mechanism, its relationship to turbulence cascade, the formation of a finite-time singularity, helicity dynamics, and aeroacoustic noise generation.
For the entire collection see [Zbl 1489.76002].Flow control for unmanned air vehicleshttps://zbmath.org/1491.760252022-09-13T20:28:31.338867Z"Greenblatt, David"https://zbmath.org/authors/?q=ai:greenblatt.david"Williams, David R."https://zbmath.org/authors/?q=ai:williams.david-r-eSummary: The pervasiveness of unmanned air vehicles (UAVs), from insect to airplane scales, combined with active flow control maturity, has set the scene for vehicles that differ markedly from present-day configurations. Nano and micro air vehicles, with characteristic Reynolds numbers typically less than \(10^5\), rely on periodically generated leading-edge vortices for lift generation, propulsion, and maneuvering. This is most commonly achieved by mechanical flapping or pulsed plasma actuation. On larger UAVs, with Reynolds numbers greater than \(10^5\), externally driven and autonomous fluidic systems continue to dominate. These include traditional circulation control techniques, autonomous synthetic jets, and discrete sweeping jets. Plasma actuators have also shown increased technological maturity. Energy efficiency is a major challenge, whether it be batteries and power electronics on nano and micro air vehicles or acceptably low compressor bleed on larger UAVs. Further challenges involve the development of aerodynamic models based on experiments or numerical simulations, as well as flight dynamics models.
For the entire collection see [Zbl 1489.76002].Cattaneo-LTNE effects on the stability of Brinkman convection in an anisotropic porous layerhttps://zbmath.org/1491.760262022-09-13T20:28:31.338867Z"Hema, M."https://zbmath.org/authors/?q=ai:hema.m"Shivakumara, I. S."https://zbmath.org/authors/?q=ai:shivakumara.i-s"Ravisha, M."https://zbmath.org/authors/?q=ai:ravisha.mSummary: The stability of Brinkman local thermal nonequilibrium anisotropic porous convection under the impact of Cattaneo law of heat conduction in solid is investigated. In the analysis, anisotropies in permeability and thermal (solid and fluid phases) conductivities are highlighted. Condition for stationary onset and oscillatory onset is obtained by carrying out linear instability analysis. A novel result is that the instability occurs through oscillatory mode against the stationary convection perceived in the absence of Cattaneo effect. The relative magnitudes of governing parameters on the initiation of oscillatory instability are delineated in detail. The thermal and mechanical anisotropies inflict stabilizing and destabilizing effects on the onset, respectively. The influence of mechanical anisotropy, thermal anisotropy of fluid, thermal relaxation time parameters and the Darcy number is to broaden the size of convection cells whereas thermal anisotropy of the solid and the Darcy-Prandtl number demonstrate a mixed behaviour. A first order amplitude equation is derived separately for steady and overstable modes by performing a weak nonlinear stability analysis using a modified multiscale method. Depending on the values of governing parameters, it is seen that the stationary mode bifurcates subcritically and supercritically, while the oscillatory mode always bifurcates supercritically.Finite rotating and translating vortex sheetshttps://zbmath.org/1491.760272022-09-13T20:28:31.338867Z"Protas, Bartosz"https://zbmath.org/authors/?q=ai:protas.bartosz"Llewellyn Smith, Stefan G."https://zbmath.org/authors/?q=ai:llewellyn-smith.stefan-g"Sakajo, Takashi"https://zbmath.org/authors/?q=ai:sakajo.takashiSummary: We consider the rotating and translating equilibria of open finite vortex sheets with endpoints in two-dimensional potential flows. New results are obtained concerning the stability of these equilibrium configurations which complement analogous results known for unbounded, periodic and circular vortex sheets. First, we show that the rotating and translating equilibria of finite vortex sheets are linearly unstable. However, while in the first case unstable perturbations grow exponentially fast in time, the growth of such perturbations in the second case is algebraic. In both cases the growth rates are increasing functions of the wavenumbers of the perturbations. Remarkably, these stability results are obtained entirely with analytical computations. Second, we obtain and analyse equations describing the time evolution of a straight vortex sheet in linear external fields. Third, it is demonstrated that the results concerning the linear stability analysis of the rotating sheet are consistent with the infinite aspect ratio limit of the stability results known for Kirchhoff's ellipse [\textit{A. E. H. Love}, Proc. Lond. Math. Soc. 25, 18--42 (1894; JFM 25.1467.02); \textit{T. B. Mitchell} and \textit{L. F. Rossi}, Phys. Fluids 20, No. 5, Paper No. 054103, 12 p. (2008; Zbl 1182.76523)] and that the solutions we obtained accounting for the presence of external fields are also consistent with the infinite aspect ratio limits of the analogous solutions known for vortex patches.Advection versus diffusion in Richtmyer-Meshkov mixinghttps://zbmath.org/1491.760282022-09-13T20:28:31.338867Z"Doss, Forrest W."https://zbmath.org/authors/?q=ai:doss.forrest-wSummary: The Richtmyer-Meshkov (RM) instability is one of the most severe degradation mechanisms for inertial confinement fusion (ICF), and mitigating it has been a priority for the global ICF effort. In this Letter, the instability's ability to atomically mix is linked to its background decay of residual turbulent energy. We show how recently derived inequalities from the mathematical theory of PDEs constrain the evolution. A model RM process at leading order may diffusively mix or retain imprints of its initial structures indefinitely, depending on initial conditions, and there exists a theoretical range of zero-mixing for certain values of parameters. The results may apply to other systems resembling scalar transport in decaying turbulence.Effects of head loss, surface tension, viscosity and density ratio on the Kelvin-Helmholtz instability in different types of pipelineshttps://zbmath.org/1491.760292022-09-13T20:28:31.338867Z"Yang, X. C."https://zbmath.org/authors/?q=ai:yang.xuechun|yang.xu-chen|yang.xia-chun|yang.xuecheng|yang.xuchi|yang.xiaochun|yang.xuechao|yang.xiaochen|yang.xiaochuan|yang.xiaochao|yang.xuechang|yang.xinchao|yang.xiuchun|yang.xiaocheng"Cao, Y. G."https://zbmath.org/authors/?q=ai:cao.yanguang|cao.yonggang|cao.yigangSummary: We report the effects of head loss, surface tension, viscosity and density ratio on the Kelvin-Helmholtz instability (KHI) in two typical pipelines, i.e., straight pipeline with different cross-sections and bend pipeline. The dynamic governing equations for upper and lower fluids in the two pipes are solved analytically. We find in the straight pipeline with different cross-sections that the relative tangential velocity of fluid decreases with the increase of the head loss, viscosity and density ratio of upper and lower fluids, but it increases with the surface tension; the amplification factor decreases with the increase of the head loss and surface tension but increases with the density ratio of upper and lower fluids; the higher the height of fluid interface is, the more both the relative tangential velocity of fluid and the amplification factor are depressed. In the bend pipeline, the critical tangential velocity of fluid is found to decrease with the increase of the head loss, viscosity and density ratio of upper and lower fluids, but it increases with the surface tension; the amplification factor increases with the head loss and density ratio of upper and lower fluids, but it decreases with the increase of the surface tension; when the elbow angle is close to \(80^\circ\), the head loss reaches its maximum. The results provide guidance for pipeline design and theoretical prediction for flooding velocity in different types of tubes.Rayleigh-Taylor and Richtmyer-Meshkov instabilities: a journey through scaleshttps://zbmath.org/1491.760302022-09-13T20:28:31.338867Z"Zhou, Ye"https://zbmath.org/authors/?q=ai:zhou.ye"Williams, Robin J. R."https://zbmath.org/authors/?q=ai:williams.robin-j-r"Ramaprabhu, Praveen"https://zbmath.org/authors/?q=ai:ramaprabhu.praveen"Groom, Michael"https://zbmath.org/authors/?q=ai:groom.michael"Thornber, Ben"https://zbmath.org/authors/?q=ai:thornber.ben"Hillier, Andrew"https://zbmath.org/authors/?q=ai:hillier.andrew"Mostert, Wouter"https://zbmath.org/authors/?q=ai:mostert.wouter"Rollin, Bertrand"https://zbmath.org/authors/?q=ai:rollin.bertrand"Balachandar, S."https://zbmath.org/authors/?q=ai:balachandar.s-raja"Powell, Phillip D."https://zbmath.org/authors/?q=ai:powell.phillip-d"Mahalov, Alex"https://zbmath.org/authors/?q=ai:mahalov.alex"Attal, N."https://zbmath.org/authors/?q=ai:attal.nSummary: Hydrodynamic instabilities such as Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities usually appear in conjunction with the Kelvin-Helmholtz (KH) instability and are found in many natural phenomena and engineering applications. They frequently result in turbulent mixing, which has a major impact on the overall flow development and other effective material properties. This can either be a desired outcome, an unwelcome side effect, or just an unavoidable consequence, but must in all cases be characterized in any model. The RT instability occurs at an interface between different fluids, when the light fluid is accelerated into the heavy. The RM instability may be considered a special case of the RT instability, when the acceleration provided is impulsive in nature such as that resulting from a shock wave. In this pedagogical review, we provide an extensive survey of the applications and examples where such instabilities play a central role. First, fundamental aspects of the instabilities are reviewed including the underlying flow physics at different stages of development, followed by an overview of analytical models describing the linear, nonlinear and fully turbulent stages. RT and RM instabilities pose special challenges to numerical modeling, due to the requirement that the sharp interface separating the fluids be captured with fidelity. These challenges are discussed at length here, followed by a summary of the significant progress in recent years in addressing them. Examples of the pivotal roles played by the instabilities in applications are given in the context of solar prominences, ionospheric flows in space, supernovae, inertial fusion and pulsed-power experiments, pulsed detonation engines and Scramjets. Progress in our understanding of special cases of RT/RM instabilities is reviewed, including the effects of material strength, chemical reactions, magnetic fields, as well as the roles the instabilities play in ejecta formation and transport, and explosively expanding flows. The article is addressed to a broad audience, but with particular attention to graduate students and researchers who are interested in the state-of-the-art in our understanding of the instabilities and the unique issues they present in the applications in which they are prominent.Effect of water vorticity on wind-generated gravity waves in finite depthhttps://zbmath.org/1491.760312022-09-13T20:28:31.338867Z"Abid, Malek"https://zbmath.org/authors/?q=ai:abid.malek"Kharif, Christian"https://zbmath.org/authors/?q=ai:kharif.christianSummary: The generation of wind waves at the surface of an established underlying vertically sheared water flow, of constant vorticity, is considered. A particular attention is paid to the role of the vorticity in water on wind-wave generation in finite depth. The present theoretical results are compared with experimental data obtained by \textit{I. R. Young} and \textit{L. A. Verhagen} [``The growth of fetch limited waves in water of finite depth. I: Total energy and peak frequency'', Coastal Eng. 29, No. 1--2, 47--78 (1996; \url{doi:10.1016/S0378-3839(96)00006-3})], in the shallow Lake George (Australia), and the least squares fit of these data by \textit{I. R. Young} [``The growth rate of finite depth wind-generated waves'', ibid. 32, No. 2--3, 181--195 (1997; \url{doi:10.1016/S0378-3839(97)81749-8})]. It is shown that without vorticity in water, there is a deviation between theory and experimental data. However, a good agreement between the theory and the fit of experimental data is obtained when negative vorticity is taken into account. Furthermore, it is shown that the amplitude growth rate increases with vorticity and depth. A limit to the wave energy growth, corresponding to the vanishing of the growth rate, is obtained. The corresponding limiting wave age is derived in a closed form showing its explicit dependence on vorticity and depth. The limiting wave age is found to increase with both vorticity and depth.Transverse bifurcation of viscous slow MHD shockshttps://zbmath.org/1491.760322022-09-13T20:28:31.338867Z"Barker, Blake"https://zbmath.org/authors/?q=ai:barker.blake"Monteiro, Rafael"https://zbmath.org/authors/?q=ai:monteiro.rafael-a"Zumbrun, Kevin"https://zbmath.org/authors/?q=ai:zumbrun.kevin-rSummary: We study by a combination of analytical and numerical Evans function techniques multi-D viscous and inviscid stability and associated transverse bifurcation of planar slow Lax MHD shocks in a channel with periodic boundary conditions. Notably, this includes the first multi-D numerical Evans function study for viscous MHD. Our results suggest that, rather than a planar shock, a nonplanar traveling wave with the same normal velocity is the typical mode of propagation in the slow Lax mode. Moreover, viscous and inviscid stability transitions appear to agree, answering (for this particular model and setting) an open question of \textit{K. Zumbrun} and \textit{D. Serre} [Indiana Univ. Math. J. 48, No. 3, 937--992 (1999; Zbl 0944.76027)].Convective, absolute and global azimuthal magnetorotational instabilitieshttps://zbmath.org/1491.760332022-09-13T20:28:31.338867Z"Mishra, A."https://zbmath.org/authors/?q=ai:mishra.amrutmayee|mishra.abinash|mishra.arijit|mishra.ankit|mishra.akshat|mishra.arvind-kumar|mishra.anwesha|mishra.awadhesh-kumar|mishra.amardeep|mishra.amrita|mishra.amarendra|mishra.aditya-mani|mishra.amit-kumar|mishra.abhishek-c|mishra.amitabh|mishra.apurva|mishra.aseem-k|mishra.ashok-kumar|mishra.asim-kumar|mishra.arti|mishra.ajit|mishra.akansha|mishra.alok-kumar|mishra.amiya|mishra.aditi|mishra.aurosish|mishra.anju|mishra.apoorva|mishra.anshuman|mishra.arunima|mishra.anurag|mishra.anil-kumar|mishra.asitav|mishra.arabinda|mishra.amruta|mishra.anand-k|mishra.ambuj-kumar|mishra.akash-k|mishra.avdesh|mishra.akshaya-kumar|mishra.ashish|mishra.asmita|mishra.asha-s|mishra.amar-p|mishra.alpna|mishra.arindam|mishra.aashwin-ananda|mishra.ajay-k|mishra.akhilesh-k|mishra.arunodaya-raj"Mamatsashvili, G."https://zbmath.org/authors/?q=ai:mamatsashvili.g-r"Galindo, V."https://zbmath.org/authors/?q=ai:galindo.vladimir"Stefani, F."https://zbmath.org/authors/?q=ai:stefani.frankSummary: We study the convective and absolute forms of azimuthal magnetorotational instability (AMRI) in a cylindrical Taylor-Couette (TC) flow with an imposed azimuthal magnetic field. We show that the domain of the convective AMRI is wider than that of the absolute AMRI. Actually, it is the absolute instability which is the most relevant and important for magnetic TC flow experiments. The absolute AMRI, unlike the convective one, stays in the device, displaying a sustained growth that can be experimentally detected. We also study the global AMRI in a TC flow of finite height using direct numerical simulation and find that its emerging butterfly-type structure -- a spatio-temporal variation in the form of axially upward and downward travelling waves -- is in a very good agreement with the linear analysis, which indicates the presence of two dominant absolute AMRI modes in the flow giving rise to this global butterfly pattern.Breathers, cascading instabilities and Fermi-Pasta-Ulam-Tsingou recurrence of the derivative nonlinear Schrödinger equation: effects of `self-steepening' nonlinearityhttps://zbmath.org/1491.760342022-09-13T20:28:31.338867Z"Yin, H. M."https://zbmath.org/authors/?q=ai:yin.khin-m|yin.huiming|yin.hui-min"Chow, K. W."https://zbmath.org/authors/?q=ai:chow.kwok-wing|chow.ka-wing|chow.kong-wingSummary: Breathers, modulation instability and recurrence phenomena are studied for the derivative nonlinear Schrödinger equation, which incorporates second order dispersion, cubic nonlinearity and self-steepening effect. By insisting on periodic boundary conditions, a cascading process will occur where initially small higher order Fourier modes can grow alongside with lower order modes. Typically a breather is first observed when all modes attain roughly the same order of magnitude. Beyond the formation of the first breather, analytical formula of spatially periodic but temporally localized breather ceases to be a valid indicator. However, numerical simulations display Fermi-Pasta-Ulam-Tsingou type recurrence. Self-steepening effect plays a crucial role in the dynamics, as it induces motion of the breather and generates chaotic behavior of the Fourier coefficients. Theoretically, correlation between breather motion and the Lax pair formulation is made. Physically, quantitative assessments of wave profile evolution are made for different initial conditions, e.g. random noise versus modulation instability mode of maximum growth rate. Potential application to fluid mechanics is discussed.Nozzle dynamics and wavepackets in turbulent jetshttps://zbmath.org/1491.760352022-09-13T20:28:31.338867Z"Kaplan, Oğuzhan"https://zbmath.org/authors/?q=ai:kaplan.oguzhan"Jordan, Peter"https://zbmath.org/authors/?q=ai:jordan.peter"Cavalieri, André V. G."https://zbmath.org/authors/?q=ai:cavalieri.andre-v-g"Brès, Guillaume A."https://zbmath.org/authors/?q=ai:bres.guillaume-aSummary: We study a turbulent jet issuing from a cylindrical nozzle to characterise coherent structures evolving in the turbulent boundary layer. The analysis is performed using data from a large-eddy simulation of a Mach 0.4 jet. Azimuthal decomposition of the velocity field in the nozzle shows that turbulent kinetic energy predominantly resides in high azimuthal wavenumbers; the first three azimuthal wavenumbers, that are important for sound generation, contain much lower, but non-zero amplitudes. Using two-point statistics, low azimuthal modes in the nozzle boundary layer are shown to exhibit significant correlations with modes of the same order in the free-jet region. Spectral proper orthogonal decomposition is used to distill a low-rank approximation of the flow dynamics. This reveals the existence of tilted coherent structures within the nozzle boundary layer and shows that these are coupled with wavepackets in the jet. The educed nozzle boundary-layer structures are modelled using a global resolvent analysis of the mean flow inside the nozzle to determine the most amplified flow responses using the linearised Navier-Stokes system. It is shown that the most-energetic nozzle structures can be successfully described with optimal resolvent response modes, whose associated forcing modes are observed to tilt against the nozzle boundary layer, suggesting that the Orr mechanism underpins these organised, turbulent, boundary-layer structures.On a mechanism of near-wall reverse flow formation in a turbulent duct flowhttps://zbmath.org/1491.760362022-09-13T20:28:31.338867Z"Zaripov, Dinar"https://zbmath.org/authors/?q=ai:zaripov.dinar"Ivashchenko, Vladislav"https://zbmath.org/authors/?q=ai:ivashchenko.vladislav"Mullyadzhanov, Rustam"https://zbmath.org/authors/?q=ai:mullyadzhanov.rustam"Li, Renfu"https://zbmath.org/authors/?q=ai:li.renfu"Mikheev, Nikolay"https://zbmath.org/authors/?q=ai:mikheev.nikolay"Kähler, Christian J."https://zbmath.org/authors/?q=ai:kahler.christian-jSummary: We address the issue of the generation mechanism of near-wall reverse flow (NWRF) events in a fully developed turbulent duct flow using direct numerical simulations and particle image velocimetry at a relatively low Reynolds number \(Re_\tau \simeq 200\). The analysis demonstrates the existence of a large-scale high-momentum flow structure originating upstream of a NWRF region. We propose a conceptual model of the NWRF formation and suggest that they are caused by intensive hairpin vortices incipient at the interface between large-scale high- and low-momentum flow regions identified using a conditional averaging procedure. The similarity of a flow topology associated with the NWRF region for \(Re_\tau \simeq 200\) with those for \(Re_\tau \simeq 1000\) [\textit{R. C. Chin} et al., ``Conditionally averaged flow topology about a critical point pair in the skin friction field of pipe flows using direct numerical simulations'', Phys. Rev. Fluids 3, No. 11, Article ID 114607, 13 p. (2018; \url{doi:10.1103/PhysRevFluids.3.114607})] and \(550 \leqslant Re_\tau \leqslant 2000\) [\textit{J. I. Cardesa} et al., J. Fluid Mech. 880, Paper No. R3, 11 p. (2019; Zbl 1430.76291)] indicates the generality of the proposed mechanism.Theoretical and numerical analysis of a simple model derived from compressible turbulencehttps://zbmath.org/1491.760372022-09-13T20:28:31.338867Z"Gavrilyuk, Sergey"https://zbmath.org/authors/?q=ai:gavrilyuk.sergey-l"Hérard, Jean-Marc"https://zbmath.org/authors/?q=ai:herard.jean-marc"Hurisse, Olivier"https://zbmath.org/authors/?q=ai:hurisse.olivier"Toufaili, Ali"https://zbmath.org/authors/?q=ai:toufaili.aliSummary: Turbulent compressible flows are encountered in many industrial applications, for instance when dealing with combustion or aerodynamics. This paper is dedicated to the study of a simple turbulent model for compressible flows. It is based on the Euler system with an energy equation and turbulence is accounted for with the help of an algebraic closure that impacts the thermodynamical behavior. Thereby, no additional PDE is introduced in the Euler system. First, a detailed study of the model is proposed: hyperbolicity, structure of the waves, nature of the fields, existence and uniqueness of the Riemann problem. Then, numerical simulations are proposed on the basis of existing finite-volume schemes. These simulations allow to perform verification test cases and more realistic explosion-like test cases with regards to the turbulence level.Mixing and combustion in a laminar shear layer with imposed counterflowhttps://zbmath.org/1491.760382022-09-13T20:28:31.338867Z"Sirignano, William A."https://zbmath.org/authors/?q=ai:sirignano.william-aSummary: Three-dimensional, steady laminar flow structures with mixing, chemical reaction, normal strain and shear strain representative of turbulent combustion are analysed. A mixing layer is subjected to counterflow in the transverse \(y\)- and \(z\)-directions providing the important practical interaction of shear-strain rate with normal-strain rate. Larger consequences for mixing rates and burning rates occur than would appear with shear strain or normal strain alone. The three characteristic times for chemical reaction, normal strain and shear strain are cast through two ratios: a Damköhler number based on rate of shear strain and a ratio of rate of normal strain to rate of shear strain. Reduction to a one-dimensional similar form is obtained with density and property variations. A generalization is found extending the Crocco integral for non-unitary Prandtl number and for imposed normal strain. A diffusion flamelet model with combined shear and normal strains is developed. Another similar solution is obtained for a configuration with a dominant diffusion flame and a weaker fuel-rich premixed flame. A conserved scalar is cast as the independent variable giving an alternative description. The imposed normal strain decreases mixing-layer thickness and increases scalar gradients and transport rates. Diffusion control is possible for partially premixed flames in the multi-branched flame situation. The imposition of shear strain and thereby vorticity on the counterflow can have a substantial consequence, indicating the need for flamelet models with both shear strain and normal strain.Evolution equations for the decomposed components of displacement speed in a reactive scalar fieldhttps://zbmath.org/1491.760392022-09-13T20:28:31.338867Z"Yu, R."https://zbmath.org/authors/?q=ai:yu.rixin"Nilsson, T."https://zbmath.org/authors/?q=ai:nilsson.thommie"Fureby, C."https://zbmath.org/authors/?q=ai:fureby.christer"Lipatnikov, A. N."https://zbmath.org/authors/?q=ai:lipatnikov.andrei-nikolaevichSummary: The study of a turbulent premixed flame often involves analysing quantities conditioned to different iso-surfaces of a reactive scalar field. Under the influence of turbulence, such a surface is deformed and translated. To track the surface motion, the displacement speed (\(S_d\)) of the scalar field respective to the local flow velocity is widely used and this quantity is currently receiving growing attention. Inspired by the apparent benefits from a simple decomposition of \(S_d\) into contributions due to (i) curvature, (ii) normal diffusion and (iii) chemical reaction, this work aims at deriving and exploring new evolution equations for these three contributions averaged over the reaction surface. Together with a previously obtained \(S_d\)-evolution equation, the three new equations are presented in a form that emphasizes the decomposition of \(S_d\) into three terms. This set of equations is also supplemented with a curvature-evolution equation, hence providing a new perspective to link the flame topology and its propagation characteristics. Using two direct numerical simulation databases obtained from constant-density and variable-density reaction waves, all the derived equations and the term-wise decomposition relations are demonstrated to hold numerically. Comparison of the simulated results indicates that the thermal expansion weakly affects the key terms in the considered evolution equations. Thermal expansion can cause variations in the averaged \(S_d\) and its decomposed parts through multiple routes more than introducing a dilatation term. The flow plays a major role to influence the key terms in all equations except the curvature one, due to a cancellation between negatively and positively curved surface elements.Ensemble gradient for learning turbulence models from indirect observationshttps://zbmath.org/1491.760402022-09-13T20:28:31.338867Z"Ströfer, Carlos A. Michelén"https://zbmath.org/authors/?q=ai:michelen-strofer.carlos-a"Zhang, Xin-Lei"https://zbmath.org/authors/?q=ai:zhang.xinlei"Xiao, Heng"https://zbmath.org/authors/?q=ai:xiao.hengSummary: Training data-driven turbulence models with high fidelity Reynolds stress can be impractical and recently such models have been trained with velocity and pressure measurements. For gradient-based optimization, such as training deep learning models, this requires evaluating the sensitivities of the RANS equations. This paper explores the use of an ensemble approximation of the sensitivities of the RANS equations in training data-driven turbulence models with indirect observations. A deep neural network representing the turbulence model is trained using the network's gradients obtained by backpropagation and the ensemble approximation of the RANS sensitivities. Different ensemble approximations are explored and a method based on explicit projection onto the sample space is presented. As validation, the gradient approximations from the different methods are compared to that from the continuous adjoint equations. The ensemble approximation is then used to learn different turbulence models from velocity observations. In all cases, the learned model predicts improved velocities. However, it was observed that once the sensitivity of the velocity to the underlying model becomes small, the approximate nature of the ensemble gradient hinders further optimization of the underlying model. The benefits and limitations of the ensemble gradient approximation are discussed, in particular as compared to the adjoint equations.The attachment angle of a sonic line to the streamlined surfacehttps://zbmath.org/1491.760412022-09-13T20:28:31.338867Z"Sizykh, G. B."https://zbmath.org/authors/?q=ai:sizykh.grigorii-bSummary: This work considers the angle of the sonic-line attachment to the surface in flows with uniform fields of entropy and total enthalpy. A rigorous study of the Euler equations (without the use of asymptotic, numerical, and other approximate methods) is carried out. Plane-parallel and nonswirling axisymmetric flows are considered. It is shown that the attachment angle of the sonic line depends on the curvature of the surface. If the surface is convex towards the flow, then the attachment angle on the subsonic side is strictly greater than \(90 \degree \). If the surface is concave towards the flow, then the attachment angle on the subsonic side is strictly less than \(90 \degree \). The attachment to a straight section of the surface in a plane-parallel flow always occurs along the normal. Similarly, only the attachment along the normal is possible if the sonic line attaches to a straight generatrix parallel to the axis of symmetry in nonswirling axisymmetric flows. For the case when the straight generatrix is not parallel to the axis of symmetry, it is shown that the attachment angle from the sonic side can only be either \(90 \degree \) (attachment along the normal) or \(0 \degree \) (attachment along the tangent).A kinetic shock layer in the spreading plane of a lifting-body apparatushttps://zbmath.org/1491.760422022-09-13T20:28:31.338867Z"Ankudinov, A. L."https://zbmath.org/authors/?q=ai:ankudinov.a-l.2Summary: In this paper, we propose an effective computational mathematical interpretation of the problem of the nonequilibrium flow of a polyatomic gas in a kinetic thin viscous shock layer near a blunt body in the plane of its symmetry. The correlation of flows in the kinetic and Navier-Stokes thin viscous shock layer on the frontal spreading line, which allows constructing the solution of the kinetic problem based entirely on the Navier-Stokes equations, is indicated. Using the proposed approach, heat transfer on the wall along the entire spreading line of a model of an aerospace aircraft of lifting-body type was numerically studied. The calculation results are compared with the data of the tunnel experiment.Transition study for asymmetric reflection between moving incident shock waveshttps://zbmath.org/1491.760432022-09-13T20:28:31.338867Z"Wang, Miao-Miao"https://zbmath.org/authors/?q=ai:wang.miaomiao"Wu, Zi-Niu"https://zbmath.org/authors/?q=ai:wu.ziniuSummary: The transition criteria seen from the ground frame are studied in this paper for asymmetrical reflection between shock waves moving at constant linear speed. To limit the size of the parameter space, these criteria are considered in detail for the reduced problem where the upper incident shock wave is moving and the lower one is steady, and a method is provided for extension to the general problem where both the upper and lower ones are unsteady. For the reduced problem, we observe that, in the shock angle plane, shock motion lowers or elevates the von Neumann condition in a global way depending on the direction of shock motion, and this change becomes less important for large shock angle. The effect of shock motion on the detachment condition, though small, displays non-monotonicity. The shock motion changes the transition criteria through altering the effective Mach number and shock angle, and these effects add for small shock angle and mutually cancel for large shock angle, so that shock motion has a less important effect for large shock angle. The role of the effective shock angle is not monotonic on the detachment condition, explaining the observed non-monotonicity for the role of shock motion on the detachment condition. Furthermore, it is found that the detachment condition has a wavefunction form that can be approximated as a hybrid of a sinusoidal function and a linear function of the shock angle.Structure-preserving discretization of a coupled heat-wave system, as interconnected port-Hamiltonian systemshttps://zbmath.org/1491.760442022-09-13T20:28:31.338867Z"Haine, Ghislain"https://zbmath.org/authors/?q=ai:haine.ghislain"Matignon, Denis"https://zbmath.org/authors/?q=ai:matignon.denisSummary: The heat-wave system is recast as the coupling of port-Hamiltonian subsystems (pHs), and discretized in a structure-preserving way by the partitioned finite element method (PFEM) [\textit{F. L. Cardoso-Ribeiro} et al., IMA J. Math. Control Inf. 38, No. 2, 493--533 (2021; Zbl 1475.93051); ``A structure-preserving Partitioned Finite Element Method for the 2D wave equation'', IFAC-PapersOnLine 51, No. 3, 119--124 (2018; \url{doi:10.1016/j.ifacol.2018.06.033})]. Then, depending on the geometric configuration of the two domains, different asymptotic behaviours of the energy of the coupled system can be recovered at the numerical level, assessing the validity of the theoretical results of \textit{X. Zhang} and \textit{E. Zuazua} [Arch. Ration. Mech. Anal. 184, No. 1, 49--120 (2007; Zbl 1178.74075)].
For the entire collection see [Zbl 1482.94007].The macroelement analysis for axisymmetric Stokes equationshttps://zbmath.org/1491.760452022-09-13T20:28:31.338867Z"Lee, Young-Ju"https://zbmath.org/authors/?q=ai:lee.youngju"Li, Hengguang"https://zbmath.org/authors/?q=ai:li.hengguangSummary: We consider the mixed finite element approximation of the axisymmetric Stokes problem (ASP) on a bounded polygonal domain in the \(rz\)-plane. Standard stability results on mixed methods do not apply due to the singular coefficients in the differential operator and due to the singular or vanishing weights in the associated function spaces. We develop new finite element analysis in these weighted spaces, and propose macroelement conditions that are sufficient to ensure the well-posedness of the mixed methods for the ASP. These conditions are local, relatively easy to verify, and therefore will be useful for validating the stability of a variety of mixed finite element methods. These new conditions can not only re-verify existing stable mixed methods for the ASP, but also lead to the discovery of new stable conservative mixed methods. We report numerical test results that confirm the theory.A study of several artificial viscosity models within the discontinuous Galerkin frameworkhttps://zbmath.org/1491.760462022-09-13T20:28:31.338867Z"Yu, Jian"https://zbmath.org/authors/?q=ai:yu.jian"Hesthaven, Jan S."https://zbmath.org/authors/?q=ai:hesthaven.jan-sSummary: Dealing with strong shocks while retaining low numerical dissipation traditionally has been one of the major challenges for high order methods like discontinuous Galerkin (DG). In the literature, shock capturing models have been designed for DG based on various approaches, such as slope limiting, (H)WENO reconstruction, a posteriori sub-cell limiting, and artificial viscosity, among which a subclass of artificial viscosity methods are compared in the present work. Four models are evaluated, including a dilation-based model, a highest modal decay model, an averaged modal decay model, and an entropy viscosity model. Performance for smooth, non-smooth and broadband problems are examined with typical one- and two-dimensional cases.Evaluation of selected finite-difference and finite-volume approaches to rotational shallow-water flowhttps://zbmath.org/1491.760472022-09-13T20:28:31.338867Z"Holm, Håvard H."https://zbmath.org/authors/?q=ai:holm.havard-h"Brodtkorb, André R."https://zbmath.org/authors/?q=ai:brodtkorb.andre-rigland"Broström, Göran"https://zbmath.org/authors/?q=ai:brostrom.goran"Christensen, Kai H."https://zbmath.org/authors/?q=ai:christensen.kai-haakon"Sætra, Martin L."https://zbmath.org/authors/?q=ai:saetra.martin-lSummary: The shallow-water equations in a rotating frame of reference are important for capturing geophysical flows in the ocean. In this paper, we examine and compare two traditional finite-difference schemes and two modern finite-volume schemes for simulating these equations. We evaluate how well they capture the relevant physics for problems such as storm surge and drift trajectory modelling, and the schemes are put through a set of six test cases. The results are presented in a systematic manner through several tables, and we compare the qualitative and quantitative performance from a cost-benefit perspective. Of the four schemes, one of the traditional finite-difference schemes performs best in cases dominated by geostrophic balance, and one of the modern finite-volume schemes is superior for capturing gravity-driven motion. The traditional finite-difference schemes are significantly faster computationally than the modern finite-volume schemes.A consistent and conservative phase-field method for multiphase incompressible flowshttps://zbmath.org/1491.760482022-09-13T20:28:31.338867Z"Huang, Ziyang"https://zbmath.org/authors/?q=ai:huang.ziyang"Lin, Guang"https://zbmath.org/authors/?q=ai:lin.guang"Ardekani, Arezoo M."https://zbmath.org/authors/?q=ai:ardekani.arezoo-mSummary: In the present study, a consistent and conservative Phase-Field method, including both the model and scheme, is developed for multiphase flows with an arbitrary number of immiscible and incompressible fluid phases. The \textit{consistency of mass conservation} and the \textit{consistency of mass and momentum transport} are implemented to address the issue of physically coupling the Phase-Field equation, which locates different phases, to the hydrodynamics. These two consistency conditions, as illustrated, provide the ``optimal'' coupling because (i) the new momentum equation resulting from them is Galilean invariant and implies the kinetic energy conservation, regardless of the details of the Phase-Field equation, and (ii) failures of satisfying the second law of thermodynamics or the \textit{consistency of reduction} of the multiphase flow model only result from the same failures of the Phase-Field equation but are not due to the new momentum equation. Physical interpretation of the consistency conditions and their formulations are first provided, and general formulations that are obtained from the consistency conditions and independent of the interpretation of the velocity are summarized. Then, the present consistent and conservative multiphase flow model is completed by selecting a reduction consistent Phase-Field equation. Several novel techniques are developed to inherit the physical properties of the multiphase flows after discretization, including the gradient-based phase selection procedure, the momentum conservative method for the surface force, and the general theorems to preserve the consistency conditions on the discrete level. Equipped with those novel techniques, a consistent and conservative scheme for the present multiphase flow model is developed and analyzed. The scheme satisfies the consistency conditions, conserves the mass and momentum, and assures the summation of the volume fractions to be unity, on the fully discrete level and for an arbitrary number of phases. All those properties are numerically validated. Numerical applications demonstrate that the present model and scheme are robust and effective in studying complicated multiphase dynamics, especially for those with large-density ratios.Numerical solver for the Boltzmann equation with self-adaptive collision operatorshttps://zbmath.org/1491.760492022-09-13T20:28:31.338867Z"Cai, Zhenning"https://zbmath.org/authors/?q=ai:cai.zhenning"Wang, Yanli"https://zbmath.org/authors/?q=ai:wang.yanliEfficient spectral method for stable stratified power-law fluid flows with dispersion over convectively heated truncated cone in a non-Darcy porous mediumhttps://zbmath.org/1491.760502022-09-13T20:28:31.338867Z"RamReddy, Ch."https://zbmath.org/authors/?q=ai:ramreddy.chetteti|reddy.ch-ram"Srivastav, Abhinava"https://zbmath.org/authors/?q=ai:srivastav.abhinavaSummary: This problem deals with the power-law fluid flow with thermally stable stratification in a non-Darcy porous medium over a convectively heated truncated cone and this work is very useful in actual and applied circumstances due to presence of non-linear Boussinesq approximation. The combined thermal diffusivity is taken as the addition of molecular diffusivity and diffusivity related to mechanical dispersion. Local non-similarity technique and spectral local linearization method are applied to solve the governing equations. A convergence test for this scheme is performed and validation of methodology is given by comparing the results in special cases with already established results. It is noted that the proposed combined scheme is an efficient algorithm with faster convergence and it acts as an alternative tool for regular numerical techniques to solve non-linear boundary value problems that occur frequently in industrial and engineering applications. The major conclusion of this study is that the magnitude of skin friction coefficient and Nusselt number are very much influenced with the presence and absence of Biot number, thermal stratification and thermal dispersion for the power-law fluids and strongly depend on the non-linear density temperature parameter.A hybrid immersed boundary-lattice Boltzmann method for simulation of viscoelastic fluid flows interaction with complex boundarieshttps://zbmath.org/1491.760512022-09-13T20:28:31.338867Z"Sedaghat, M. H."https://zbmath.org/authors/?q=ai:sedaghat.mohammad-h|sedaghat.maral-khadem"Bagheri, A. A. H."https://zbmath.org/authors/?q=ai:bagheri.a-a-h"Shahmardan, M. M."https://zbmath.org/authors/?q=ai:shahmardan.m-m"Norouzi, M."https://zbmath.org/authors/?q=ai:norouzi.mohammadjavad"Khoo, B. C."https://zbmath.org/authors/?q=ai:khoo.boo-cheong"Jayathilake, P. G."https://zbmath.org/authors/?q=ai:jayathilake.p-gSummary: In this study, a numerical technique based on the Lattice Boltzmann method is presented to model viscoelastic fluid interaction with complex boundaries which are commonly seen in biological systems and industrial practices. In order to accomplish numerical simulation of viscoelastic fluid flows, the Newtonian part of the momentum equations is solved by the Lattice Boltzmann Method (LBM) and the divergence of the elastic tensor, which is solved by the finite difference method, is added as a force term to the governing equations. The fluid-structure interaction forces are implemented through the Immersed Boundary Method (IBM). The numerical approach is validated for Newtonian and viscoelastic fluid flows in a straight channel, a four-roll mill geometry as well as flow over a stationary and rotating circular cylinder. Then, a numerical simulation of Oldroyd-B fluid flow around a confined elliptical cylinder with different aspect ratios is carried out for the first time. Finally, the present numerical approach is used to simulate a biological problem which is the mucociliary transport process of human respiratory system. The present numerical results are compared with appropriate analytical, numerical and experimental results obtained from the literature.Bayesian learning of stochastic dynamical modelshttps://zbmath.org/1491.760522022-09-13T20:28:31.338867Z"Lu, Peter"https://zbmath.org/authors/?q=ai:lu.peter-j"Lermusiaux, Pierre F. J."https://zbmath.org/authors/?q=ai:lermusiaux.pierre-f-jSummary: A new methodology for rigorous Bayesian learning of high-dimensional stochastic dynamical models is developed. The methodology performs parallelized computation of marginal likelihoods for multiple candidate models, integrating over all state variable and parameter values, and enabling a principled Bayesian update of model distributions. This is accomplished by leveraging the dynamically orthogonal (DO) evolution equations for uncertainty prediction in a dynamic stochastic subspace and the Gaussian Mixture Model-DO filter for inference of nonlinear state variables and parameters, using reduced-dimension state augmentation to accommodate models featuring uncertain parameters. Overall, the joint Bayesian inference of the state, model equations, geometry, boundary conditions, and initial conditions is performed. Results are exemplified using two high-dimensional, nonlinear simulated fluid and ocean systems. For the first, limited measurements of fluid flow downstream of an obstacle are used to perform joint inference of the obstacle's shape, the Reynolds number, and the \(\mathcal{O}(10^5)\) fluid velocity state variables. For the second, limited measurements of the concentration of a microorganism advected by an uncertain flow are used to perform joint inference of the microorganism's reaction equation and the \(\mathcal{O}(10^5)\) microorganism concentration and ocean velocity state variables. When the observations are sufficiently informative about the learning objectives, we find that our posterior model probabilities correctly identify either the true model or the most plausible models, even in cases where a human would be challenged to do the same.A fast convergent semi-analytic method for an electrohydrodynamic flow in a circular cylindrical conduithttps://zbmath.org/1491.760532022-09-13T20:28:31.338867Z"Abukhaled, Marwan"https://zbmath.org/authors/?q=ai:abukhaled.marwan-i"Khuri, S. A."https://zbmath.org/authors/?q=ai:khuri.suheil-aSummary: A semi-analytical solution of the nonlinear boundary value problem that models the electrohydrodynamic flow of a fluid in an ion drag configuration in a circular cylindrical conduit is presented. An integral operator expressed in terms of Green's function is constructed then followed by an application of fixed point theory to generate a highly accurate semi-analytical expression of the fluid velocity for all possible values of relevant parameters. A proof of convergence for the proposed method, based on the contraction mapping principle, is presented. Numerical simulations and comparison with other analytical methods confirm that the proposed approach is convergent, stable, and highly accurate.Multisymplectic variational integrators for fluid models with constraintshttps://zbmath.org/1491.760542022-09-13T20:28:31.338867Z"Demoures, François"https://zbmath.org/authors/?q=ai:demoures.francois"Gay-Balmaz, François"https://zbmath.org/authors/?q=ai:gay-balmaz.francoisSummary: We present a structure preserving discretization of the fundamental spacetime geometric structures of fluid mechanics in the Lagrangian description in 2D and 3D. Based on this, multisymplectic variational integrators are developed for barotropic and incompressible fluid models, which satisfy a discrete version of Noether theorem. We show how the geometric integrator can handle regular fluid motion in vacuum with free boundaries and constraints such as the impact against an obstacle of a fluid flowing on a surface. Our approach is applicable to a wide range of models including the Boussinesq and shallow water models, by appropriate choice of the Lagrangian.
For the entire collection see [Zbl 1482.94007].Metriplectic integrators for dissipative fluidshttps://zbmath.org/1491.760552022-09-13T20:28:31.338867Z"Kraus, Michael"https://zbmath.org/authors/?q=ai:kraus.michaelSummary: Many systems from fluid dynamics and plasma physics possess a so-called metriplectic structure, that is the equations are comprised of a conservative, Hamiltonian part, and a dissipative, metric part. Consequences of this structure are conservation of important quantities, such as mass, momentum and energy, and compatibility with the laws of thermodynamics, e.g., monotonic dissipation of entropy and existence of a unique equilibrium state.
For simulations of such systems to deliver accurate and physically correct results, it is important to preserve these relations and conservation laws in the course of discretisation. This can be achieved most easily not by enforcing these properties directly, but by preserving the underlying abstract mathematical structure of the equations, namely their metriplectic structure. From that, the conservation of the aforementioned desirable properties follows automatically.
This paper describes a general and flexible framework for the construction of such metriplectic structure-preserving integrators, that facilitates the design of novel numerical methods for systems from fluid dynamics and plasma physics.
For the entire collection see [Zbl 1482.94007].Off-grid DOA estimation based on alternating iterative weighted least squares for acoustic vector hydrophone arrayhttps://zbmath.org/1491.760562022-09-13T20:28:31.338867Z"Wang, Weidong"https://zbmath.org/authors/?q=ai:wang.weidong"Zhang, Qunfei"https://zbmath.org/authors/?q=ai:zhang.qunfei"Shi, Wentao"https://zbmath.org/authors/?q=ai:shi.wentao"Tan, Weijie"https://zbmath.org/authors/?q=ai:tan.weijie"Mao, Linlin"https://zbmath.org/authors/?q=ai:mao.linlinSummary: In this paper, an alternating iterative weighted least squares method is proposed to handle the off-grid issue in sparsity-based direction of arrival (DOA) estimation for acoustic vector hydrophone (AVH) array. Firstly, the off-grid model via AVH array is formulated by introducing a bias parameter into the signal model. Secondly, the reconstructed interference plus noise covariance matrix is calculated as the weighting term. Then, a novel objective function with respect to the sparse signal and the unknown bias parameter is developed based on weighted least squares. Finally, the closed-form solutions of the sparse signal and the unknown bias parameter are deduced. Simulation results reveal that compared with the state-of-the-art algorithms, the proposed method improves the DOA estimation accuracy in the presence of a coarse sample grid and has a faster convergence speed. Furthermore, the effectiveness and robustness of the proposed method are verified by the underwater experimental results.An adaptive virtual element method for incompressible flowhttps://zbmath.org/1491.760572022-09-13T20:28:31.338867Z"Wang, Ying"https://zbmath.org/authors/?q=ai:wang.ying|wang.ying.2|wang.ying.8|wang.ying.4|wang.ying.5|wang.ying.6|wang.ying.3|wang.ying.1"Wang, Gang"https://zbmath.org/authors/?q=ai:wang.gang.5|wang.gang.4|wang.gang.1|wang.gang.3|wang.gang|wang.gang.2"Wang, Feng"https://zbmath.org/authors/?q=ai:wang.feng.3|wang.feng.4|wang.feng.1|wang.feng.2Summary: In this paper, we firstly present and analyze a residual-type a posteriori error estimator for a low-order virtual element discretization for the Stokes problem on general polygonal meshes. We prove that this estimator yields globally upper and locally lower bounds for the discretization error. Then, we extend the estimator to the Navier-Stokes problem. In order to deal with the case of small viscosity, we modify the discrete bilinear form following the idea of variational multiscale method. Since the virtual element method naturally handles hanging nodes, the mesh refinement can exploit them without any local refinement to recover mesh conformity. A series of benchmark tests are reported to verify the effectiveness and flexibility of the designed error estimator when it is combined with adaptive mesh refinement.A Cartesian-to-curvilinear coordinate transformation in modified ghost fluid method for compressible multi-material flowshttps://zbmath.org/1491.760582022-09-13T20:28:31.338867Z"Xu, Liang"https://zbmath.org/authors/?q=ai:xu.liang"Lou, Hao"https://zbmath.org/authors/?q=ai:lou.hao"Yang, Wubing"https://zbmath.org/authors/?q=ai:yang.wubing"Liu, Tiegang"https://zbmath.org/authors/?q=ai:liu.tiegangSummary: Modified ghost fluid method (MGFM) provides us an effective manner to simulate compressible multi-material flows. In most cases, the applications are limited in relatively simple geometries described by Cartesian grids. In this paper, the MGFM treatment with the level set (LS) technique is extended to curvilinear coordinate systems. The chain rule of differentiation (applicable to general curvilinear coordinates) and the orthogonal transformation (applicable to orthogonal curvilinear coordinates) are utilized to deduce the Cartesian-to-curvilinear coordinate transformation, respectively. The relationship between these two transformations for the extension of the LS/MGFM algorithm is analyzed in theory. It is shown that these two transformations are equivalent for orthogonal curvilinear grids. The extension of the LS/MGFM algorithm using the chain rule has a wider range of applications, as there is essentially no requirement for the orthogonality of the grids. Several challenging problems in two- or three-dimensions are utilized to validate the developed algorithm in curvilinear coordinates. The results indicate that this algorithm enables a simple and effective implementation for simulating interface evolutions, as in Cartesian coordinate systems. It has the potential to be applied in more complex computational domains.Maximal regularity for compressible two-fluid systemhttps://zbmath.org/1491.760592022-09-13T20:28:31.338867Z"Piasecki, Tomasz"https://zbmath.org/authors/?q=ai:piasecki.tomasz"Zatorska, Ewelina"https://zbmath.org/authors/?q=ai:zatorska.ewelinaThe authors studied a compressible two-fluid Navier-Stokes type system with a single velocity field and algebraic closure for the pressure. They showed that regular solutions in a \(L^p-L^q\) maximal regularity setting exist both locally and globally in time, under additional smallness assumptions on the initial data. The interesting proof relies on appropriate transformation of the original problem, application of Lagrangian coordinates and maximal regularity estimates for associated linear problem.
Reviewer: Teng Wang (Beijing)Global strong solution to the Cauchy problem of 1D viscous two-fluid model without any domination conditionhttps://zbmath.org/1491.760602022-09-13T20:28:31.338867Z"Gao, Xiaona"https://zbmath.org/authors/?q=ai:gao.xiaona"Guo, Zhenhua"https://zbmath.org/authors/?q=ai:guo.zhenhua"Li, Zilai"https://zbmath.org/authors/?q=ai:li.zilaiSummary: In this paper, we consider the Cauchy problem to the compressible two-fluid Navier-Stokes equations in one-dimensional space allowing vacuum. It is shown that the compressible two-fluid Navier-Stokes equations admit global strong solution with the large initial value and no the domination condition1 which was posed in [\textit{A. Vasseur} et al., J. Math. Pures Appl. (9) 125, 247--282 (2019; Zbl 1450.76033)], when the initial vacuum can be permitted inside the region. Note that this result is proved without any smallness conditions on the initial value.Homogenization of the evolutionary compressible Navier-Stokes-Fourier system in domains with tiny holeshttps://zbmath.org/1491.760612022-09-13T20:28:31.338867Z"Pokorný, Milan"https://zbmath.org/authors/?q=ai:pokorny.milan"Skříšovský, Emil"https://zbmath.org/authors/?q=ai:skrisovsky.emilSummary: We study the homogenization of the evolutionary compressible Navier-Stokes-Fourier system in a bounded three-dimensional domain perforated with a large number of very tiny holes. We show that under suitable assumptions on the smallness and distribution of the holes the limit system remains the same in the unperforated domain. One of the main novelty in the paper consists in the treatment of the entropy inequality and thus the paper also improves the related result in the steady case from \textit{Y. Lu} and \textit{M. Pokorný} [J. Differ. Equations 278, 463--492 (2021; Zbl 1458.35043)].A simplified lumped parameter model for pneumatic tubeshttps://zbmath.org/1491.760622022-09-13T20:28:31.338867Z"Kamiński, Zbigniew"https://zbmath.org/authors/?q=ai:kaminski.zbigniewSummary: Tubes are commonly used in pneumatic systems for transferring energy and control signals. Using the control volume method, a mathematical tube model has been developed, which takes into account the effect of resistance, capacitance and inertance on the dynamic properties of control and supply circuits of pneumatic systems. The adequacy of the computer model developed in Matlab/Simulink was verified by comparing the results of simulation studies with the results of experimental tests of airflow through tubes of varying diameter and length. The advantage of the computer model is the capability to model pneumatic systems under varying conditions of heat exchange with the environment by changing the coefficient of the polytropic process coefficient.Physical modelling of a long pneumatic transmission line: models of successively decreasing complexity and their experimental validationhttps://zbmath.org/1491.760632022-09-13T20:28:31.338867Z"Kern, Richard"https://zbmath.org/authors/?q=ai:kern.richardSummary: There exist a significant number of models, which describe the dynamics of pneumatic transmission lines. The models are based on different assumptions and, thereby, vary in the physical phenomena they incorporate. These assumptions made are not always stated clearly and the models are rarely validated with measurement data. The aim of this article is to present multiple distributed parameter models that, starting from a physical system description, successively decrease in complexity and finally result in a rather simple system representation. Data, both from simulation studies as well as from a pneumatic test bench, serve as a quantitative validation of these assumptions. Based on a detailed discussion of the different models, this article aims at facilitating the choice of an appropriate model for a given task where the effect of long pneumatic transmission lines cannot be neglected and a trade-off between accuracy and complexity is required.Accuracy of a low Mach number model for time-harmonic acousticshttps://zbmath.org/1491.760642022-09-13T20:28:31.338867Z"Mercier, J.-F."https://zbmath.org/authors/?q=ai:mercier.jean-francoisA method to enhance the noise robustness of correlation velocity measurement using discrete wavelet transformhttps://zbmath.org/1491.760652022-09-13T20:28:31.338867Z"Son, Pong-Chol"https://zbmath.org/authors/?q=ai:son.pong-chol"Kim, Kyong-Il"https://zbmath.org/authors/?q=ai:kim.kyong-il"Choe, Kyong-Chol"https://zbmath.org/authors/?q=ai:choe.kyong-chol"Kye, Hyok-Il"https://zbmath.org/authors/?q=ai:kye.hyok-ilCorrelation velocity measurement techniques are efficiently used to measure the velocity of underwater vehicles, and the maximum correlation coefficient is an important parameter of correlation velocity measurement. In this paper, the relationship between the signal-to-noise ratio (SNR) of the received signal and the maximum value of the correlation matrix is considered, and the maximum correlation coefficient equation according to SNR is presented. Especially, a wavelet thresholding denoising method is successfully used to improve SNR so that the noise robustness of correlation velocity measurement is proposed, and the modified maximum correlation coefficient equation according to SNR is provided accordingly. Simulation results show that the new method of correlation velocity measurement using wavelet thresholding could get the largest maximum correlation coefficients according to SNR steadily compared with the classical method. In particular, the performance improvements in correlation velocity log (CVL) operating under low SNR below 6 dB are more significant.
Reviewer: Yankui Sun (Beijing)Mixed convection fluid flow over a vertical cone saturated porous media with double dispersion and injection/suction effectshttps://zbmath.org/1491.760662022-09-13T20:28:31.338867Z"Meena, Om Prakash"https://zbmath.org/authors/?q=ai:meena.om-prakash"Janapatla, Pranitha"https://zbmath.org/authors/?q=ai:janapatla.pranitha"Srinivasacharya, D."https://zbmath.org/authors/?q=ai:srinivasacharya.darbhashayanam|srinivasacharya.darbhasayanamSummary: This study reflects the combined impact of double dispersion and injection/suction on mixed convection flow over a vertical cone in an incompressible viscous fluid-saturated porous medium. The governing equations of the model are non-dimensionalized throughout the appropriate transformations and received non-similarity equations are solved numerically via bivariate Chebyshev spectral collocation quasi-linearization method. Computations are reported here graphically to analyze the impact of governing parameters at the different stream-wise locations on the velocity, temperatures, and concentration profiles, like Prandtl number, Schmidt number, buoyancy parameter, injection and suction parameter, thermal dispersion, and Solutal dispersion parameters. Skin friction, heat, and mass transfer rates are also reported in graphical and tabular form. To establish the efficiency of the adopted numerical technique, we have made a comparison with the earlier published results and found them to be of great consent. The residual analysis study also illustrated, which proves the convergence of the present results.A route to chaos in Rayleigh-Bénard heat convectionhttps://zbmath.org/1491.760672022-09-13T20:28:31.338867Z"Hsia, Chun-Hsiung"https://zbmath.org/authors/?q=ai:hsia.chun-hsiung"Nishida, Takaaki"https://zbmath.org/authors/?q=ai:nishida.takaakiSummary: We use numerical methods to study the global bifurcation diagrams of the Bénard convection problem. In our computations, we include a huge number of Fourier modes of stream function and temperature function so that our results reflect more reality of the dynamics of the Rayleigh-Bénard heat convection. Our results confirm that the period doubling scenario is a route to chaos.Thermophoresis on free convective unsteady/steady Couette fluid flow with mass transferhttps://zbmath.org/1491.760682022-09-13T20:28:31.338867Z"Jha, Basant K."https://zbmath.org/authors/?q=ai:jha.basant-k"Sani, Hadiza N."https://zbmath.org/authors/?q=ai:sani.hadiza-nSummary: This article reports analytical as well as numerical solutions for fully developed unsteady natural convection in a Couette flow with transfer of mass due to thermophoresis. The time dependent model describes a physical situation which is solved using a finite difference Scheme that is implicit, backward in time and centered in space. The steady state version of the present physical situation has been solved exactly. The influence of controlling parameters on dimensionless velocity, concentration, skin-frictions and Sherwood number are demonstrated through graphs and tables. Graphical results show that Schmidt number should be greater than 0.6 for thermophoresis to be effective in air. The numerical results reveal that the ratio of convective mass transfer to diffusive mass transfer increases with increases in thermophoresis coefficient and time until it finally reaches its steady-state value.Effect of non-inertial acceleration on Brinkman-Bénard convection in water-copper nanoliquid-saturated porous enclosureshttps://zbmath.org/1491.760692022-09-13T20:28:31.338867Z"Siddheshwar, P. G."https://zbmath.org/authors/?q=ai:siddheshwar.pradeep-g"Veena, B. N."https://zbmath.org/authors/?q=ai:veena.b-nSummary: In the present paper we have considered rotating porous tall, square and shallow enclosures heated from below. Linear and non-linear analyses are made using a minimal representation by Fourier trigonometric series. The study is done for realistic boundary condition. Thermophysical properties of water-copper nanoliquid as a function of properties of water as base liquid, copper as nanoparticle and 30\% glass fiber reinforced polycarbonate as porous medium are obtained from either phenomenological laws or mixture theory. Non-existence of oscillatory convection is discussed. The range for the existence of unicellular convection is mentioned. The effects of Brinkman number (\( \varLambda \)), porous parameter (\( \sigma^2\)), aspect ratio (\(A\)) and volume fraction (\( \chi \)) in the presence of rotation on the onset of convection and heat transfer are studied and illustrated graphically. The analytically intractable Lorenz model is derived and transformed into the tractable Ginzburg-Landau equation using the multiscales method. The definition of Ozoe heat transfer parameter is introduced to discuss the rate of heat transfer enhancement or reduction. It is observed that \(Ta\), \( \varLambda\) and \(\sigma^2\) have stabilizing effect on the system and thereby leading to diminished heat transfer whereas \(A\) and \(\chi\) have destabilizing effect on the system and thereby leading to increased heat transfer. Among the three enclosures considered in the study enhanced heat transfer takes place in tall enclosure followed by square and shallow enclosures respectively. It is further observed that presence of nanoparticles advances the onset of convection and enhances the heat transfer. The results of the paper are compared with previous existing results in the absence of rotation and the good agreement is found between them.Influence of electroosmosis mechanism and chemical reaction on convective flow over an exponentially accelerated platehttps://zbmath.org/1491.760702022-09-13T20:28:31.338867Z"Vijayaragavan, R."https://zbmath.org/authors/?q=ai:vijayaragavan.rajaram"Bharathi, V."https://zbmath.org/authors/?q=ai:bharathi.v-subbiah|bharathi.v-vijaya"Prakash, J."https://zbmath.org/authors/?q=ai:prakash.jagdish|prakash.j-ravi|prakash.jitendra|prakash.j-s|prakash.jyoti|prakash.jaiSummary: This article is primarily attained to study the electric double layer (EDL) phenomena and chemical reaction effects on unsteady natural convection flow through exponentially accelerated plate. The Poisson Boltzmann equation is used to derive the electroosmosis mechanism. The special effect of Lorentz and Darcy forces are considered in the proposed mathematical model. Governing equations of proposed model is linearized through Debye-Hückel linearization and dimensionless analysis. The system of nonlinear partial differential equations are solved with the help of Laplace transform technique. Further, the Nusselt number and Sherwood number are also derived. The graphical outcomes for velocity, temperature, concentration, Nusselt number and Sherwood number are illustrated with the help of Matlab software. Validation of the present solution is obtained by Laplace transform method which is compared with numerical solution obtained by finite difference with the help of MATLAB code. It is seen that the velocity profile is unequivocally reliance with attractive field and EDL thickness. It is also found that chemical reaction parameter significantly pretends on temperature distribution. This idea can be equipped for being applied in different complex frameworks where the electroosmosis stream can be moved by CPUs gadget.Persisting asymmetry in the probability distribution function for a random advection-diffusion equation in impermeable channelshttps://zbmath.org/1491.760712022-09-13T20:28:31.338867Z"Camassa, Roberto"https://zbmath.org/authors/?q=ai:camassa.roberto"Ding, Lingyun"https://zbmath.org/authors/?q=ai:ding.lingyun"Kilic, Zeliha"https://zbmath.org/authors/?q=ai:kilic.zeliha"McLaughlin, Richard M."https://zbmath.org/authors/?q=ai:mclaughlin.richard-mSummary: In this paper, we study the effect of impermeable boundaries on the symmetry properties of a random passive scalar field advected by random flows. We focus on a broad class of nonlinear shear flows multiplied by a stationary, Ornstein-Uhlenbeck (OU) time varying process, including some of their limiting cases, such as Gaussian white noise or plug flows. For the former case with linear shear, recent studies [\textit{R. Camassa} et al., Physica D 400, Article ID 132124, 32 p. (2019; Zbl 1453.60116)] numerically demonstrated that the decaying passive scalar's long time limiting probability distribution function (PDF) could be negatively skewed in the presence of impermeable channel boundaries, in contrast to rigorous results in free space which established the limiting PDF is positively skewed [\textit{R. M. McLaughlin} and \textit{A. J. Majda}, Phys. Fluids 8, No. 2, 536--547 (1996; Zbl 1023.76560)]. Here, the role of boundaries in setting the long time limiting skewness of the PDF is established rigorously for the above class using the long time asymptotic expansion of the \(N\)-point correlator of the random field obtained from the ground state eigenvalue perturbation approach proposed in [\textit{J. C. Bronski} and \textit{R. M. McLaughlin}, Phys. Fluids 9, No. 1, 181--190 (1997; Zbl 1185.76678)]. Our analytical result verifies the conclusion for the linear shear flow obtained from numerical simulations in [Camassa et al., loc. cit.]. Moreover, we demonstrate that the limiting distribution is negatively skewed for any shear flow at sufficiently low Péclet number. We demonstrate the convergence of the Ornstein-Uhlenbeck case to the white noise case in the limit \(\gamma \to \infty\) of the OU damping parameter, which generalizes the results for free space in [\textit{S. G. Resnick}, Dynamical problems in non-linear advective partial differential equations, The University of Chicago (PhD Thesis) (1996)] to the channel domain problem. We show that the long time limit of the first three moments depends explicitly on the value of \(\gamma\), which is in contrast to the conclusion in [\textit{E. Vanden Eijnden}, Commun. Pure Appl. Math. 54, No. 9, 1146--1167 (2001; Zbl 1036.76025)] for the limiting PDF in free space. To find a benchmark for theoretical analysis, we derive the exact formula of the \(N\)-point correlator for a flow with no spatial dependence and Gaussian temporal fluctuation, generalizing the results of \textit{J. C. Bronski} et al. [J. Stat. Phys. 128, No. 4, 927--968 (2007; Zbl 1185.76693)]. The long time analysis of this formula is consistent with our theory for a general shear flow. All results are verified by Monte-Carlo simulations.Various formulations and approximations of incompressible fluid motions in porous mediahttps://zbmath.org/1491.760722022-09-13T20:28:31.338867Z"Brenier, Yann"https://zbmath.org/authors/?q=ai:brenier.yannSummary: We first recall various formulations and approximations for the motion of an incompressible fluid, in the well-known setting of the Euler equations. Then, we address incompressible motions in porous media, through the Muskat system, which is a friction dominated first order analog of the Euler equations for inhomogeneous incompressible fluids subject to an external potential.The combined effects of wall properties and space porosity on MHD two-phase peristaltic slip transport through planar channelshttps://zbmath.org/1491.760732022-09-13T20:28:31.338867Z"Eldesoky, I. M."https://zbmath.org/authors/?q=ai:eldesoky.islam-m"Abumandour, R. M."https://zbmath.org/authors/?q=ai:abumandour.r-m"Kamel, M. H."https://zbmath.org/authors/?q=ai:kamel.m-h"Abdelwahab, E. T."https://zbmath.org/authors/?q=ai:abdelwahab.e-tSummary: In this article, a theoretical investigation is analyzing the effects of the complaint wall properties, the slip conditions, the space porosity, and the transverse magnetic field on the magnetohydrodynamic peristaltic transport of viscous compressible flow carrying out some rigid spherical suspension particles flowing through space porous medium in a horizontal elastic rectangular channel. The flexible channel walls are taken as a sinusoidal wave. The expressions describing the peristaltic transport are mathematically analyzed using the perturbation technique with a small amplitude wave ratio. The analytical study describes the influence of various wall parameters such as damping force, wall tension, and wall elasticity and flow parameters as compressibility parameter, slip parameter, suspension parameter, Reynolds number, space porosity, and magnetic field parameter on the net axial velocity. The reversal flow occurs at the channel core and boundaries due to the slip and the magnetic field effects. Biological, geophysical, and industrial fluid dynamics applications are important models for the peristaltic transport described in this work.Coupled hydro-mechanical modeling of gas flow in shale matrix considering the fractal characteristics of nanoporeshttps://zbmath.org/1491.760742022-09-13T20:28:31.338867Z"Gao, Qi"https://zbmath.org/authors/?q=ai:gao.qi"Cheng, Yuanfang"https://zbmath.org/authors/?q=ai:cheng.yuanfang"Han, Songcai"https://zbmath.org/authors/?q=ai:han.songcai"Li, Yang"https://zbmath.org/authors/?q=ai:li.yang.5|li.yang.8|li.yang.6|li.yang.7"Yan, Chuanliang"https://zbmath.org/authors/?q=ai:yan.chuanliang"Han, Zhongying"https://zbmath.org/authors/?q=ai:han.zhongyingOn the influence of state selection on mass conservation in dynamic vapour compression cycle modelshttps://zbmath.org/1491.760752022-09-13T20:28:31.338867Z"Laughman, Christopher R."https://zbmath.org/authors/?q=ai:laughman.christopher-r"Qiao, Hongtao"https://zbmath.org/authors/?q=ai:qiao.hongtaoSummary: Many dynamic models of vapour compression systems experience nonphysical variations in the total refrigerant mass contained in the system when common modelling approaches are used. Rather than using the traditional state variables of pressure and specific enthalpy, the use of density as a state variable can eliminate these variations. The reasons for these variations are explained, and a set of test models is developed to study the effect of the state variable selection on the overall system charge. Results from both a simplified cycle model and a realistic air-source heat pump model indicate that this alternative approach has significant benefits for maintaining a fixed mass of refrigerant in the cycle.Fundamental fluid dynamics challenges in inkjet printinghttps://zbmath.org/1491.760762022-09-13T20:28:31.338867Z"Lohse, Detlef"https://zbmath.org/authors/?q=ai:lohse.detlefSummary: Inkjet printing is the most widespread technological application of microfluidics. It is characterized by its high drop productivity, small volumes, and extreme reproducibility. This review gives a synopsis of the fluid dynamics of inkjet printing and discusses the main challenges for present and future research. These lie both on the printhead side -- namely, the detailed flow inside the printhead, entrained bubbles, the meniscus dynamics, wetting phenomena at the nozzle plate, and jet formation -- and on the receiving substrate side -- namely, droplet impact, merging, wetting of the substrate, droplet evaporation, and drying. In most cases the droplets are multicomponent, displaying rich physicochemical hydrodynamic phenomena. The challenges on the printhead side and on the receiving substrate side are interwoven, as optimizing the process and the materials with respect to either side alone is not enough: As the same ink (or other jetted liquid) is used and as droplet frequency and size matter on both sides, the process must be optimized as a whole.
For the entire collection see [Zbl 1489.76002].On the shape of air-liquid interfaces with surface tension that bound rigidly rotating liquids in partially filled containershttps://zbmath.org/1491.760772022-09-13T20:28:31.338867Z"Ramé, Enrique"https://zbmath.org/authors/?q=ai:rame.enrique"Weinstein, Steven J."https://zbmath.org/authors/?q=ai:weinstein.steven-j"Barlow, Nathaniel S."https://zbmath.org/authors/?q=ai:barlow.nathaniel-sSummary: The interface shape of a fluid in rigid body rotation about its axis and partially filling the container is often the subject of a homework problem in the first graduate fluids class. In that problem, surface tension is neglected, the interface shape is parabolic and the contact angle boundary condition is not satisfied in general. When surface tension is accounted for, the shapes exhibit much richer dependencies as a function of rotation velocity. We analyze steady interface shapes in rotating right-circular cylindrical containers under rigid body rotation in zero gravity. We pay special attention to shapes near criticality, in which the interface, or part thereof, becomes straight and parallel to the axis of rotation at certain specific rotational speeds. We examine geometries where the container is axially infinite and derive properties of their solutions. We then examine in detail two special cases of menisci in a cylindrical container: a meniscus spanning the cross-section and a meniscus forming a bubble. In each case, we develop exact solutions for the respective axial lengths as infinite series in powers of appropriate rotation parameters, and we find the respective asymptotic behaviors as the shapes approach their critical configuration. Finally, we apply the method of asymptotic approximants to yield analytical expressions for the axial lengths of the menisci over the whole range of rotation speeds. In this application, the analytical solution is employed to examine errors introduced by the assumption that the interface is a right circular cylinder; this assumption is key to the spinning bubble method used to measure surface tension.The retraction of jetted slender viscoelastic liquid filamentshttps://zbmath.org/1491.760782022-09-13T20:28:31.338867Z"Sen, Uddalok"https://zbmath.org/authors/?q=ai:sen.uddalok"Datt, Charu"https://zbmath.org/authors/?q=ai:datt.charu"Segers, Tim"https://zbmath.org/authors/?q=ai:segers.tim"Wijshoff, Herman"https://zbmath.org/authors/?q=ai:wijshoff.herman"Snoeijer, Jacco H."https://zbmath.org/authors/?q=ai:snoeijer.jacco-h"Versluis, Michel"https://zbmath.org/authors/?q=ai:versluis.michel"Lohse, Detlef"https://zbmath.org/authors/?q=ai:lohse.detlefSummary: Long and slender liquid filaments are produced during inkjet printing, which can subsequently either retract to form a single droplet, or break up to form a primary droplet and one or more satellite droplets. These satellite droplets are undesirable since they degrade the quality and reproducibility of the print, and lead to contamination within the enclosure of the print device. Existing strategies for the suppression of satellite droplet formation include, among others, adding viscoelasticity to the ink. In the present work, we aim to improve the understanding of the role of viscoelasticity in suppressing satellite droplets in inkjet printing. We demonstrate that very dilute viscoelastic aqueous solutions (concentrations \(\sim\) 0.003 \% wt. polyethylene oxide, corresponding to nozzle Deborah number \(De_n\sim 3\)) can suppress satellite droplet formation. Furthermore, we show that, for a given driving condition, upper and lower bounds of polymer concentration exist, within which satellite droplets are suppressed. Satellite droplets are formed at concentrations below the lower bound, while jetting ceases for concentrations above the upper bound (for fixed driving conditions). Moreover, we observe that, with concentrations in between the two bounds, the filaments retract at velocities larger than the corresponding Taylor-Culick velocity for the Newtonian case. We show that this enhanced retraction velocity can be attributed to the elastic tension due to polymer stretching, which builds up during the initial jetting phase. These results shed some light on the complex interplay between inertia, capillarity and viscoelasticity for retracting liquid filaments, which is important for the stability and quality of inkjet printing of polymer solutions.Continuum and molecular dynamics studies of the hydrodynamics of colloids straddling a fluid interfacehttps://zbmath.org/1491.760792022-09-13T20:28:31.338867Z"Maldarelli, Charles"https://zbmath.org/authors/?q=ai:maldarelli.charles"Donovan, Nicole T."https://zbmath.org/authors/?q=ai:donovan.nicole-t"Ganesh, Subramaniam Chembai"https://zbmath.org/authors/?q=ai:ganesh.subramaniam-chembai"Das, Subhabrata"https://zbmath.org/authors/?q=ai:das.subhabrata"Koplik, Joel"https://zbmath.org/authors/?q=ai:koplik.joelSummary: Colloid-sized particles (10 nm-\(10 \mu\) m in characteristic size) adsorb onto fluid interfaces, where they minimize their interfacial energy by straddling the surface, immersing themselves partly in each phase bounding the interface. The energy minimum achieved by relocation to the surface can be orders of magnitude greater than the thermal energy, effectively trapping the particles into monolayers, allowing them freedom only to translate and rotate along the surface. Particles adsorbed at interfaces are models for the understanding of the dynamics and assembly of particles in two dimensions and have broad technological applications, importantly in foam and emulsion science and in the bottom-up fabrication of new materials based on their monolayer assemblies. In this review, the hydrodynamics of the colloid motion along the surface is examined from both continuum and molecular dynamics frameworks. The interfacial energies of adsorbed particles is discussed first, followed by the hydrodynamics, starting with isolated particles followed by pairwise and multiple particle interactions. The effect of particle shape is emphasized, and the role played by the immersion depth and the surface rheology is discussed; experiments illustrating the applicability of the hydrodynamic studies are also examined.
For the entire collection see [Zbl 1489.76002].Development of mathematical modeling of multi-phase flow of Casson rheological fluid: theoretical approachhttps://zbmath.org/1491.760802022-09-13T20:28:31.338867Z"Nazeer, Mubbashar"https://zbmath.org/authors/?q=ai:nazeer.mubbashar"Hussain, Farooq"https://zbmath.org/authors/?q=ai:hussain.farooq"Hameed, M. K."https://zbmath.org/authors/?q=ai:hameed.m-k"Ijaz Khan, M."https://zbmath.org/authors/?q=ai:khan.m-ijaz"Ahmad, Fayyaz"https://zbmath.org/authors/?q=ai:ahmad.fayyaz"Malik, M. Y."https://zbmath.org/authors/?q=ai:malik.muhammad-yousaf"Shi, Qiu-Hong"https://zbmath.org/authors/?q=ai:shi.qiuhongSummary: Theoretical stud of a rheological fluid suspended with two types of nanoparticles through a steep channel is presented in this article. Each suspension is formed by using the non-Newtonian Casson fluid model as the base liquid. Particulate flows are generated mainly due to the effects of gravitational force. In addition to this, the contribution of transversely applied magnetic fields is also considered. Further, the flow dynamics of Casson multiphase flows are compared with the ones suspended with the Newtonian fluid model. A closed-form solution is obtained for the mathematical modeled nonlinear partial differential equations which are transformed into a set of the ordinary differential equation. Separate expressions for volumetric flow rate and pressure gradient have been formulated, as well. Numerical results computed in the different tables show that Hafnium particles gain more momentum than crystal particles. Owing to, many engineering applications of highly thick multiphase flows, such as in chemical and textile industries, it is evident that Casson multiphase suspensions are quite suitable for coating purposes. Moreover, magnetized multiphase flows are compared with the previous investigation as the limiting case for the validation.Irreversibility analysis for axisymmetric nanomaterial flow towards a stretched surfacehttps://zbmath.org/1491.760812022-09-13T20:28:31.338867Z"Song, Ying-Qing"https://zbmath.org/authors/?q=ai:song.yingqing"Shah, Faqir"https://zbmath.org/authors/?q=ai:shah.faqir"Khan, Sohail A."https://zbmath.org/authors/?q=ai:khan.sohail-ahmed"Khan, M. Ijaz"https://zbmath.org/authors/?q=ai:khan.m-ijaz"Malik, M. Y."https://zbmath.org/authors/?q=ai:malik.muhammad-yousaf"Sun, Tian-Chuan"https://zbmath.org/authors/?q=ai:sun.tianchuanSummary: Magnetohydrodynamic axisymmetric flow of viscous nanoliquid towards a variable stretching sheet is scrutinized. Flow is generated due to nonlinear stretching. Joule heating, heat flux and dissipation are analyzed in heat expression. Random and thermophoresis diffusions are considered. Physical description of entropy generation is also accounted. Entropy generation and heat transfer analysis are scrutinized through thermodynamics laws. Furthermore chemical reaction along with Arrhenius activation energy is addressed. Ordinary differential system is obtained through suitable variables. Homotopic convergent solutions for nonlinear system is developed. Influence of flow variables on entropy rate, velocity, Bejan number, concentration and temperature are analyzed. Further velocity gradient and heat and mass transfer rates are discussed. Reduction in velocity is noticed for magnetic variable. Thermal field has an enhancing trend for magnetic and Eckert number. Larger thermophoresis variable rises the temperature. An increment in entropy rate is observed for magnetic parameter. An increment in drag force is seen for magnetic variable.Theoretical analysis of linearized non-isothermal two-dimensional model of liquid chromatography columns packed with core-shell particleshttps://zbmath.org/1491.760822022-09-13T20:28:31.338867Z"Uche, Ugochukwu David"https://zbmath.org/authors/?q=ai:uche.ugochukwu-david"Uche, Mercy"https://zbmath.org/authors/?q=ai:uche.mercySummary: A linearized single-solute two-dimensional general rate model of non-isothermal liquid chromatography for columns of cylindrical geometry packed with core-shell particles is formulated and solved analytically to investigate the effects of temperature changes. A linear system of convection-diffusion partial differential equations is developed by the model equations. The solutions of the equations are obtained by applying Hankel transformation, Laplace transformation, Eigen-decomposition method and a general method for solving ordinary differential equations. The coupling between the concentration fronts and thermal waves is illustrated and key parameters that influence the chromatography column's performance are identified. For the same system of equations for both linear and nonlinear isotherms, a finite volume scheme is applied. Moreover, the ranges of validity of the analytical results are found using the same finite volume scheme.An analysis of the unified formulation for the equilibrium problem of compositional multiphase mixtureshttps://zbmath.org/1491.760832022-09-13T20:28:31.338867Z"Ben Gharbia, Ibtihel"https://zbmath.org/authors/?q=ai:ben-gharbia.ibtihel"Haddou, Mounir"https://zbmath.org/authors/?q=ai:haddou.mounir"Tran, Quang Huy"https://zbmath.org/authors/?q=ai:tran.quang-huy"Vu, Duc Thach Son"https://zbmath.org/authors/?q=ai:vu.duc-thach-sonSummary: In this paper, we conduct a thorough mathematical analysis of the unified formulation advocated by \textit{A. Lauser} et al. [``A new approach for phase transitions in miscible multi-phase flow in porous media'', Adv. Water Res. 34, No. 8, 957--966 (2011; \url{doi:10.1016/j.advwatres.2011.04.021})] for compositional multiphase flows in porous media. The interest of this formulation lies in its potential to automatically handle the appearance and disappearance of phases. However, its practical implementation turned out to be not always robust for realistic fugacity laws associated with cubic equations of state, as shown by the first author and \textit{E. Flauraud} [``Study of compositional multiphase flow formulation using complementarity conditions'', Oil Gas Sci. Technol. 74, Article No. 43, 15 p. (2019; \url{doi:10.2516/ogst/2019012 })]. By focusing on the subproblem of phase equilibrium, we derive sufficient conditions for the existence of the corresponding system of equations. We trace back the difficulty of cubic laws to a deficiency of the Gibbs functions that comes into play due to the ``unifying'' feature of the new formulation. We propose a partial remedy for this problem by extending the domain of definition of these functions in a natural way. Besides, we highlight the crucial but seemingly unknown fact that the unified formulation encapsulates all the properties known to physicists on phase equilibrium, such as the tangent plane criterion and the minimization of the Gibbs energy of the mixture.Moisture in textileshttps://zbmath.org/1491.760842022-09-13T20:28:31.338867Z"Duprat, C."https://zbmath.org/authors/?q=ai:duprat.cedric|duprat.camilleSummary: The interactions of textiles with moisture have been thoroughly studied in textile research, while fluid mechanists and soft matter physicists have partially investigated the underlying physics phenomena. A description of liquid morphologies in fibrous assemblies allows one to characterize the associated capillary forces and their impact on textiles, and to organize their complex moisture transport dynamics. This review gathers some of the common features and fundamental mechanisms at play in textile-liquid interactions, with selected examples ranging from knitted fabrics to nonwoven paper sheets, associated with experiments on model systems.
For the entire collection see [Zbl 1489.76002].Design and simulation of mechanical ventilatorshttps://zbmath.org/1491.760852022-09-13T20:28:31.338867Z"El-Hadj, Abdellah"https://zbmath.org/authors/?q=ai:el-hadj.abdellah"Kezrane, Mohamed"https://zbmath.org/authors/?q=ai:kezrane.mohamed"Ahmad, Hijaz"https://zbmath.org/authors/?q=ai:ahmad.hijaz"Ameur, Houari"https://zbmath.org/authors/?q=ai:ameur.houari"Bin Abd Rahim, S. Zamree"https://zbmath.org/authors/?q=ai:bin-abd-rahim.s-zamree"Younsi, Abdelhakime"https://zbmath.org/authors/?q=ai:younsi.abdelhakime"Abu-Zinadah, Hanaa"https://zbmath.org/authors/?q=ai:abu-zinadah.hanaa-hSummary: During this period of COVID-19 pandemic, the lack of medical equipment (like ventilators) leads to complications arising in the medical field. A low-cost ventilator seems to be an alternative substitute to fill the lacking. This paper presents a numerical analysis for predicting the delivered parameters of a low-cost mechanical ventilator. Based on several manufactured mechanical ventilators, two proposed designs are investigated in this study. Fluid-structure interaction (FSI) analysis is used for solving any problems with the first design, and computational fluid dynamic (CFD) analysis with moving boundary is used for solving any issues with the second design. For this purpose, ANSYS Workbench platform is used to solve the set of equations. The results showed that the Ambu-bag-based mechanical ventilator exhibited difficulties in controlling ventilation variables, which certainly will cause serious health problems such as barotrauma. The mechanical ventilator based on piston-cylinder is more satisfactory with regards to delivered parameters to the patient. The ways to obtain pressure control mode (PCM) and volume control mode (VCM) are identified. Finally, the ventilator output is highly affected by inlet flow, length of the cylinder, and piston diameter.Theoretical analysis of rolling fluid turbineshttps://zbmath.org/1491.760862022-09-13T20:28:31.338867Z"Kincl, Ondřej"https://zbmath.org/authors/?q=ai:kincl.ondrej"Pavelka, Michal"https://zbmath.org/authors/?q=ai:pavelka.michal"Maršík, František"https://zbmath.org/authors/?q=ai:marsik.frantisek"Sedláček, Miroslav"https://zbmath.org/authors/?q=ai:sedlacek.miroslavDouble Magnus type wind turbinehttps://zbmath.org/1491.760872022-09-13T20:28:31.338867Z"Klimina, L. A."https://zbmath.org/authors/?q=ai:klimina.lyubov-aleksandrovna"Shalimova, E. S."https://zbmath.org/authors/?q=ai:shalimova.ekaterina-sergeevna"Dosaev, M. Z."https://zbmath.org/authors/?q=ai:dosaev.marat-z"Selyutskiy, Yu. D."https://zbmath.org/authors/?q=ai:selyutskiy.yury-d|selyutskii.yu-dSummary: A closed mathematical model of a double Magnus type wind turbine with a horizontal axis is constructed. The propellers of the turbine are supposed to rotate in opposite directions. For such a system, equations of motion are derived. In the case of dimensions of the front propeller being two times smaller than dimensions of the rear propeller, operating modes and a trapped power coefficient are found numerically.Fluid dynamics of axial turbomachinery: blade- and stage-level simulations and modelshttps://zbmath.org/1491.760882022-09-13T20:28:31.338867Z"Sandberg, Richard D."https://zbmath.org/authors/?q=ai:sandberg.richard-d"Michelassi, Vittorio"https://zbmath.org/authors/?q=ai:michelassi.vittorioSummary: The current generation of axial turbomachines is the culmination of decades of experience, and detailed understanding of the underlying flow physics has been a key factor for achieving high efficiency and reliability. Driven by advances in numerical methods and relentless growth in computing power, computational fluid dynamics has increasingly provided insights into the rich fluid dynamics involved and how it relates to loss generation. This article presents some of the complex flow phenomena occurring in bladed components of gas turbines and illustrates how simulations have contributed to their understanding and the challenges they pose for modeling. The interaction of key aerodynamic features with deterministic unsteadiness, caused by multiple blade rows, and stochastic unsteadiness, i.e., turbulence, is discussed. High-fidelity simulations of increasingly realistic configurations and models improved with help of machine learning promise to further grow turbomachinery performance and reliability and, thus, help fluid mechanics research have a greater industrial impact.
For the entire collection see [Zbl 1489.76002].Exact viscous compressible flow describing the dynamics of the atmospherehttps://zbmath.org/1491.760892022-09-13T20:28:31.338867Z"Ionescu-Kruse, Delia"https://zbmath.org/authors/?q=ai:ionescu-kruse.deliaSummary: We focus on the Navier-Stokes equations for a compressible viscous fluid -- allowing variations of the dynamic eddy viscosity only in the vertical direction -- and the continuity equation. Our problem is written in spherical coordinates, in a non-inertial rotating frame. For zonal flows, with no variations in the longitudinal direction, and in a neighbourhood of the Equator, we get a linear parabolic evolution equation that we solve by the method of separation of variables. For a dynamic eddy viscosity which decreases with height above the ground level, the velocity field obtained has an azimuthal component which depends on time and has a nonlinear dependence on the radial coordinate, and a vertical component which depends linearly on the radial coordinate.Wave propagation in rotating shallow water in the presence of small-scale topographyhttps://zbmath.org/1491.760902022-09-13T20:28:31.338867Z"Goldsmith, E. J."https://zbmath.org/authors/?q=ai:goldsmith.edward-j"Esler, J. G."https://zbmath.org/authors/?q=ai:esler.j-gSummary: The question of how finite-amplitude, small-scale topography affects small-amplitude motions in the ocean is addressed in the framework of the rotating shallow water equations. The extent to which the dispersion relations of Poincaré, Kelvin and Rossby waves are modified in the presence of topography is illuminated, using a range of numerical and analytical techniques based on the method of homogenisation. Both random and regular periodic arrays of topography are considered, with the special case of regular cylinders studied in detail, because this case allows for highly accurate analytical results. The results show that, for waves in a \(\beta\)-channel bounded by sidewalls, and for steep topographies outside of the quasi-geostrophic regime, topography acts to slow Poincaré waves slightly, Rossby waves are slowed significantly and Kelvin waves are accelerated for long waves and slowed for short waves, with the two regimes being separated by a narrow band of resonant wavelengths. The resonant band, which is due to the excitation of trapped topographic Rossby waves on each seamount, may affect any of the three wave types under the right conditions, and for physically reasonable results requires regularisation by Ekman friction. At larger topographic amplitudes, for cylindrical topography, a simple and accurate formula is given for the correction to the Rossby wave dispersion relation, which extends previous results for the quasi-geostrophic regime.Reacting multi-component fluids: regular solutions in Lorentz spaceshttps://zbmath.org/1491.760912022-09-13T20:28:31.338867Z"Mucha, Piotr Bogusław"https://zbmath.org/authors/?q=ai:mucha.piotr-boguslaw"Piasecki, Tomasz"https://zbmath.org/authors/?q=ai:piasecki.tomaszSummary: The paper deals with the analysis of a model of a multi-component fluid admitting chemical reactions. The flow is considered in the incompressible regime. The main result shows the global existence of regular solutions under the assumption of suitable smallness conditions. In order to control the solutions a special structure condition on the derivatives of chemical production functions determining the reactions is required. The existence is shown in a new critical functional framework of Lorentz spaces of type \(L_{p, r}(0, T; L_q)\), which allows to control the integral \(\int_0^\infty \|\nabla u(t)\|_\infty dt\).Asymptotic shallow models arising in magnetohydrodynamicshttps://zbmath.org/1491.760922022-09-13T20:28:31.338867Z"Alonso-Orán, Diego"https://zbmath.org/authors/?q=ai:alonso-oran.diegoSummary: In this paper, we derive new shallow asymptotic models for the free boundary plasma-vacuum problem governed by the magnetohydrodynamic equations which are vital when describing large-scale processes in flows of astrophysical plasma. More precisely, we present the magnetic analogue of the 2D Green-Naghdi equations for water waves under a weak magnetic pressure assumption in the presence of weakly sheared vorticity and magnetic currents. Our method is inspired by ideas for hydrodynamic flows developed in [\textit{A. Castro} and \textit{D. Lannes}, J. Fluid Mech. 759, 642--675 (2014; Zbl 1446.76077)] to reduce the three-dimensional dynamics of the vorticity and current to a finite cascade of two dimensional equations which can be closed at the precision of the model.Dynamo action between two rotating discshttps://zbmath.org/1491.760932022-09-13T20:28:31.338867Z"Arslan, A."https://zbmath.org/authors/?q=ai:arslan.atakan|arslan.a-muzaffer|arslan.ayse-n|arslan.ahmet-faruk|arslan.a-v|arslan.abdullah-n|arslan.ali|arslan.aykut"Mestel, A. J."https://zbmath.org/authors/?q=ai:mestel.a-jonathanSummary: Dynamo action is considered in the region between two differentially rotating infinite discs. The boundaries may be insulating, perfectly conducting or ferromagnetic. In the absence of a magnetic field, various well-known self-similar flows arise, generalising that of von Kármán. Magnetic field instabilities with the same similarity structure are sought. The kinematic eigenvalue problem is found to have growing modes for \(Re_m > R_c\simeq 100\). The growth rate is real for the perfectly conducting and ferromagnetic cases, but may be complex for insulating boundaries. As \(Re_m\to\infty\) it is shown that the dynamo can be fast or slow, depending on the flow structure. In the slow case, the growth rate is governed by a magnetic boundary layer on one of the discs. The growing field saturates in a solution to the nonlinear dynamo problem. The bifurcation is found to be subcritical and nonlinear dynamos are found for \(Re_m\gtrsim0.7R_c\). Finally, the flux of magnetic energy to large \(r\) is examined, to determine which solutions might generalise to dynamos between finite discs. It is found that the fast dynamos tend to have inward energy flux, and so are unlikely to be realised in practice. Slow dynamos with outward flux are found. It is suggested that the average rotation rate should be non-zero in practice.Inclined MHD and radiative Maxwell slip fluid flow and heat transfer due to permeable melting surface with a non-linear heat sourcehttps://zbmath.org/1491.760942022-09-13T20:28:31.338867Z"Dadheech, Amit"https://zbmath.org/authors/?q=ai:dadheech.amit"Parmar, Amit"https://zbmath.org/authors/?q=ai:parmar.amit"Olkha, Amala"https://zbmath.org/authors/?q=ai:olkha.amalaSummary: The study analyzed a non-Newtonian Maxwell fluid flow past a permeable and melting surface with non-linear thermal radiation, inclined magnetic field chemical reaction with higher-order and non-uniform heat sources effects numerically. The governing PDEs are transformed into non-linear ODEs and solved by the shooting technique based on Runge Kutta with MATLAB toolbox. The results are shown graphically and in tabular form. The apprehensions of pictorial and tabular notations are used to analyze the effect of physical parameters governing velocity, energy, and mass. The obtained result thus confirms that an excellent agreement is achieved with those available in the open literature. The outcomes are represented as a magnetic parameter, porosity parameter and Maxwell fluid parameter have reduced the momentum boundary layer thickness.Nonstationary flow of a viscous incompressible electrically conductive fluid on a rotating platehttps://zbmath.org/1491.760952022-09-13T20:28:31.338867Z"Gurchenkov, A. A."https://zbmath.org/authors/?q=ai:gurchenkov.a-aSummary: In this work, the evolution of a flow of a viscous electrically conductive fluid on a rotating plate in the presence of a magnetic field is studied. The analytical solution of three-dimensional unsteady equations of magnetohydrodynamics is presented. The velocity field and the induced magnetic field in the flow of a viscous electrically conductive fluid filling a half-space bounded by a flat wall are determined. The fluid, together with the bounding plane, rotates as a whole with a constant angular velocity around a direction not perpendicular to the plane. An unsteady flux is induced by suddenly beginning vibrations of the wall and an applied magnetic field directed perpendicular to the plane. A number of special cases of the wall motion are considered. Based on the results obtained, the individual structures of the boundary layers near the wall are investigated.Melting heat transfer of MHD micropolar fluid flow past an exponentially stretching sheet with slip and thermal radiationhttps://zbmath.org/1491.760962022-09-13T20:28:31.338867Z"Mandal, Iswar Chandra"https://zbmath.org/authors/?q=ai:mandal.iswar-chandra"Mukhopadhyay, Swati"https://zbmath.org/authors/?q=ai:mukhopadhyay.swati"Vajravelu, Kuppalapalle"https://zbmath.org/authors/?q=ai:vajravelu.kuppalapalleSummary: The effects of velocity slip and radiation on MHD flow and melting heat transfer of a micropolar fluid due to an exponentially stretched sheet are presented. By means of similarity transformations the leading partial differential equations are changed to a set of ordinary differential equations which are nonlinear. Numerical solutions of the nonlinear system of equations are then obtained by changing the boundary value problem first to an initial value problem. It is observed that the pertaining parameters have significant effects on the flow and heat transfer characteristics, which are presented and talked about in detail through their illustrations. Due to boost in the melting parameter, the fluid velocity, angular velocity and temperature are found to decrease. Fluid velocity and angular velocity both decrease with a rise in slip at the boundary but quite opposite is the effect on the temperature.Numerical simulation of radiative MHD Sutterby nanofluid flow through porous medium in the presence of Hall currents and electroosmosishttps://zbmath.org/1491.760972022-09-13T20:28:31.338867Z"Ramesh, K."https://zbmath.org/authors/?q=ai:ramesh.k-s|ramesh.k-v|ramesh.k-t|ramesh.kasilingam|ramesh.kiran"Rawal, Madhav"https://zbmath.org/authors/?q=ai:rawal.madhav"Patel, Aryaman"https://zbmath.org/authors/?q=ai:patel.aryamanSummary: Analysis of thermal and fluid phenomena based on the fluid dynamics theory leads to understanding of fundamental mechanisms in modern technologies. Thermal/fluid transport is critical to many applications, such as photothermal cancer therapy, solar thermal evaporation and polymer composites. The current study focusses to investigate the effect of magnetohydrodynamics, Hall currents and electroosmosis on the propulsion of Sutterby nanofluids in a porous microchannel. The Brownian motion and thermophoresis effects have also been considered. The governing equations for the momentum, temperature and nanoparticle volume fraction have been modified under the suitable non-dimensional quantities. The resulting dimensionless system of equations have been solved using bvp4c package in computational software MATLAB. The pictorial representations have been presented for various flow quantities with respect to sundry fluid parameters. It is noted from the investigation that, there is a decrease in fluid velocity with an increase in Hartmann number, temperature decreases with the increment in radiation parameter and nanoparticle volume fraction reduces with the increment of Prandtl number and thermophoresis parameter. The results obtained for the Sutterby nanofluid propulsion model reveal many engrossing behaviors and has many applications such as disease diagnostics and cancerous tissues destruction, and that provide a further dimension to investigate the nanofluid flow problems with thermophysical properties in two/three dimensions.On the inverse problem for Channell collisionless plasma equilibriahttps://zbmath.org/1491.760982022-09-13T20:28:31.338867Z"Allanson, Oliver"https://zbmath.org/authors/?q=ai:allanson.oliver"Troscheit, Sascha"https://zbmath.org/authors/?q=ai:troscheit.sascha"Neukirch, Thomas"https://zbmath.org/authors/?q=ai:neukirch.thomasSummary: Vlasov-Maxwell equilibria are described by the self-consistent solutions of the time-independent Maxwell equations for the real-space dynamics of electromagnetic fields and the Vlasov equation for the phase-space dynamics of particle distribution functions (DFs) in a collisionless plasma. These two systems (macroscopic and microscopic) are coupled via the source terms in Maxwell's equations, which are sums of velocity-space `moment' integrals of the particle DF. This paper considers a particular subset of solutions of the broad plasma physics problem: `the inverse problem for collisionless equilibria' (IPCE), viz. \textit{`given information regarding the macroscopic configuration of a collisionless plasma equilibrium, what self-consistent equilibrium DFs exist?'} We introduce the constants of motion approach to IPCE using the assumptions of a `modified Maxwellian' DF, and a strictly neutral and spatially one-dimensional plasma, and this is consistent with `\textit{P. J. Channell}'s method' [``Exact Vlasov-Maxwell equilibria with sheared magnetic fields'', Phys. Fluids 19, No. 10, 1541--1545 (1976; \url{doi:10.1063/1.861357})]. In such circumstances, IPCE formally reduces to the inversion of Weierstrass transformations [\textit{G. G. Bilodeau}, Duke Math. J. 29, 293--308 (1962; Zbl 0154.38003)]. These are the same transformations that feature in the initial value problem for the heat/diffusion equation. We discuss the various mathematical conditions that a candidate solution of IPCE must satisfy. One method that can be used to invert the Weierstrass transform is expansions in Hermite polynomials. Building on the results of \textit{O. Allanson} et al. [``From one-dimensional fields to Vlasov equilibria: theory and application of Hermite polynomials'', J. Plasma Phys. 82, No. 3, Article ID 905820306, 28 p. (2016; \url{doi:10.1017/S0022377816000519})], we establish under what circumstances a solution obtained by these means converges and allows velocity moments of all orders. Ever since the seminal work by \textit{I. B. Bernstein} et al. [Phys. Rev., II. Ser. 108, 546--550 (1957; Zbl 0081.44904)] on `stationary' electrostatic plasma waves, the necessary quality of non-negativity has been noted as a feature that any candidate solution of IPCE will not \textit{a priori} satisfy. We discuss this problem in the context of Channell equilibria, for magnetized plasmas.Bulk viscosity in relativistic fluids: from thermodynamics to hydrodynamicshttps://zbmath.org/1491.760992022-09-13T20:28:31.338867Z"Gavassino, L."https://zbmath.org/authors/?q=ai:gavassino.lorenzo"Antonelli, M."https://zbmath.org/authors/?q=ai:antonelli.melissa|antonelli.michele|antonelli.marco|antonelli.miranda-j|antonelli.michela|antonelli.massimo"Haskell, B."https://zbmath.org/authors/?q=ai:haskell.bTaylor dispersion in non-Darcy porous media with bulk chemical reaction: a model for drug transport in impeded blood vesselshttps://zbmath.org/1491.761002022-09-13T20:28:31.338867Z"Roy, Ashis Kumar"https://zbmath.org/authors/?q=ai:roy.ashis-kumar"Bég, O. Anwar"https://zbmath.org/authors/?q=ai:beg.o-anwar|beg.osman-anwar"Saha, Apu Kumar"https://zbmath.org/authors/?q=ai:saha.apu-kumar"Murthy, J. V. Ramana"https://zbmath.org/authors/?q=ai:murthy.j-v-ramanaSummary: The present article discusses the solute transport process in steady laminar blood flow through a non-Darcy porous medium, as a model for drug movement in blood vessels containing deposits. The Darcy-Brinkman-Forchheimer drag force formulation is adopted to mimic a sparsely packed porous domain, and the vessel is approximated as an impermeable cylindrical conduit. The conservation equations are implemented in an axisymmetric system \((R, Z)\) with suitable boundary conditions, assuming constant tortuosity and porosity of the medium. Newtonian flow is assumed, which is physically realistic for large vessels at high shear rates. The velocity field is expanded asymptotically, and the concentration field decomposed. Advection and dispersion coefficient expressions are rigorously derived. Extensive visualization of the influence of effective Péclet number, Forchheimer number, reaction parameter on velocity, asymptotic dispersion coefficient, mean concentration, and transverse concentration at different axial locations and times is provided. Increasing reaction parameter and Forchheimer number both decrease the dispersion coefficient, although the latter exhibits a linear decay. The maximum mean concentration is enhanced with greater Forchheimer numbers, although the centre of the solute cloud is displaced in the backward direction. Peak mean concentration is suppressed with the reaction parameter, although the centroid of the solute cloud remains unchanged. Peak mean concentration deteriorates over time since the dispersion process is largely controlled by diffusion at the large time, and therefore the breakthrough curve is more dispersed. A similar trend is computed with increasing Péclet number (large Péclet numbers imply diffusion-controlled transport). The computations provide some insight into a drug (pharmacological agents) reacting linearly with blood.Optimal swimmers can be pullers, pushers or neutral depending on the shapehttps://zbmath.org/1491.761012022-09-13T20:28:31.338867Z"Daddi-Moussa-Ider, Abdallah"https://zbmath.org/authors/?q=ai:daddi-moussa-ider.abdallah"Nasouri, Babak"https://zbmath.org/authors/?q=ai:nasouri.babak"Vilfan, Andrej"https://zbmath.org/authors/?q=ai:vilfan.andrej"Golestanian, Ramin"https://zbmath.org/authors/?q=ai:golestanian.raminSummary: The ability of microswimmers to deploy optimal propulsion strategies is of paramount importance for their locomotory performance and survival at low Reynolds numbers. Although for perfectly spherical swimmers minimum dissipation requires a neutral-type swimming, any departure from the spherical shape may lead the swimmer to adopt a new propulsion strategy, namely those of puller- or pusher-type swimming. In this study, by using the minimum dissipation theorem for microswimmers, we determine the flow field of an optimal nearly spherical swimmer, and show that indeed depending on the shape profile, the optimal swimmer can be a puller, pusher or neutral. Using an asymptotic approach, we find that amongst all the modes of the shape function, only the third mode determines, to leading order, the swimming type of the optimal swimmer.Propagation of a terahertz Bessel vortex beam through a homogeneous magnetized plasma slabhttps://zbmath.org/1491.780032022-09-13T20:28:31.338867Z"Li, Haiying"https://zbmath.org/authors/?q=ai:li.haiying"Ding, Wei"https://zbmath.org/authors/?q=ai:ding.wei"Liu, Jiawei"https://zbmath.org/authors/?q=ai:liu.jiawei"Ying, Ci"https://zbmath.org/authors/?q=ai:ying.ci"Bai, Lu"https://zbmath.org/authors/?q=ai:bai.lu"Wu, Zhensen"https://zbmath.org/authors/?q=ai:wu.zhensenSummary: This paper provides an analytic method to study propagation characteristics of a linearly polarized Bessel vortex beam through a homogeneous magnetized plasma slab. The incident Bessel vortex beam, as well as the reflected, transmitted and internal fields are expanded in terms of cylindrical vector wave functions (CVWFs). The effects of plasma thickness, electron density and magnetic induction strength on the contour profiles of the reflected and transmitted beams and orbital angular momentum (OAM) spectra are analyzed and discussed in detail. In particular, the magnetic induction strength has a significant impact on the polarization of the transmitted beam, but not on OAM state distribution. The channel capacity of THz OAM multiplexing decreases with an increase of plasma thickness and electron density.On the temperature equation in classical irreversible thermodynamicshttps://zbmath.org/1491.800032022-09-13T20:28:31.338867Z"Ciancio, Vincenzo"https://zbmath.org/authors/?q=ai:ciancio.vincenzoSummary: Abstract.In this paper, by using a procedure of classical irreversible thermodynamics with internal variables, some possible interactions among heat conduction and viscous-elastic flows for rheological media are studied. By introducing as an vectorial internal variable \(\boldsymbol \xi\), which influences thermal and diffusion phenomena, phenomenological equation for these variables are derived. A general vector, \(\boldsymbol J\), is introduced which assumes the role of heat flux and it is shown that, in isotropic media, \(\boldsymbol J\) can be composed of two parts and this allows to obtain a heat equation that generalizes both the Fourier equation and the Maxwell-Cattaneo-Vernotte (M-C-V) equation. A general temperature equation and the energy balance equation for viscoelastic media are obtained.Basic space plasma physicshttps://zbmath.org/1491.820012022-09-13T20:28:31.338867Z"Baumjohann, Wolfgang"https://zbmath.org/authors/?q=ai:baumjohann.wolfgang"Treumann, Rudolf A."https://zbmath.org/authors/?q=ai:treumann.rudolf-aPublisher's description: This textbook describes Earth's plasma environment from single particle motion in electromagnetic fields, with applications to Earth's magnetosphere, up to plasma wave generation and wave-particle interaction. The origin and effects of collisions and conductivities are discussed in detail, as is the formation of the ionosphere, the origin of magnetospheric convection and magnetospheric dynamics in solar wind-magnetosphere coupling, the evolution of magnetospheric storms, auroral substorms, and auroral phenomena of various kinds.
The second half of the book presents the theoretical foundation of space plasma physics, from kinetic theory of plasma through the formation of moment equations and derivation of magnetohydrodynamic theory of plasmas. The validity of this theory is elucidated, and two-fluid theory is presented in more detail. This is followed by a brief analysis of fluid boundaries, with Earth's magnetopause and bow shock as examples. The main emphasis is on the presentation of fluid and kinetic wave theory, deriving the relevant wave modes in a high temperature space plasma. Plasma instability is the most important topic in all applications and is discussed separately, including a section on thermal fluctuations. These theories are applied to the most interesting problems in space plasma physics, collisionless reconnection and collisionless shock waves with references provided. The Appendix includes the most recent developments in the theory of statistical particle distributions in space plasma, the Kappa distribution, etc, also including a section on space plasma turbulence and emphasizing on new observational developments with a dimensional derivation of the Kolmogorov spectrum, which might be instructive for the student who may worry about its origin.
The book ends with a section on space climatology, space meteorology and space weather, a new application field in space plasma physics that is of vital interest when considering the possible hazards to civilization from space.
See the reviews of the first and second editions in [Zbl 0971.82040; Zbl 1252.82001].Parametrising non-linear dark energy perturbationshttps://zbmath.org/1491.830222022-09-13T20:28:31.338867Z"Hassani, Farbod"https://zbmath.org/authors/?q=ai:hassani.farbod"L'Huillier, Benjamin"https://zbmath.org/authors/?q=ai:lhuillier.benjamin"Shafieloo, Arman"https://zbmath.org/authors/?q=ai:shafieloo.arman"Kunz, Martin"https://zbmath.org/authors/?q=ai:kunz.martin"Adamek, Julian"https://zbmath.org/authors/?q=ai:adamek.julian(no abstract)Consistent Blandford-Znajek expansionhttps://zbmath.org/1491.830272022-09-13T20:28:31.338867Z"Armas, Jay"https://zbmath.org/authors/?q=ai:armas.jay"Cai, Yangyang"https://zbmath.org/authors/?q=ai:cai.yangyang"Compère, Geoffrey"https://zbmath.org/authors/?q=ai:compere.geoffrey"Garfinkle, David"https://zbmath.org/authors/?q=ai:garfinkle.david"Gralla, Samuel E."https://zbmath.org/authors/?q=ai:gralla.samuel-e(no abstract)Cosmic microwave background anisotropy numerical solution (CMBAns). I: An introduction to \(C_l\) calculationhttps://zbmath.org/1491.830592022-09-13T20:28:31.338867Z"Das, Santanu"https://zbmath.org/authors/?q=ai:das.santanu-kumar"Phan, Anh"https://zbmath.org/authors/?q=ai:phan.anh-dung|phan.anh-vu|phan.anh-huy(no abstract)Boundary stabilization of an elastic body surrounding a viscous incompressible fluidhttps://zbmath.org/1491.930902022-09-13T20:28:31.338867Z"Do, K. D."https://zbmath.org/authors/?q=ai:do.khac-ducSummary: This paper considers the problem of boundary feedback stabilization of an elastic body surrounding a viscous incompressible fluid described by Navier-Stokes equations in three dimensional space. The paper gives a proof of global existence of a weak solution of the closed-loop system via the Galerkin method. Due to consideration of less regular initial values of the fluid velocity, the forces induced by the fluid on the elastic body are not able to bound. Therefore, the paper handles ``fluid work and fluid power'' on the elastic body in stability and convergence analysis of the closed-loop system.