Recent zbMATH articles in MSC 76Fhttps://zbmath.org/atom/cc/76F2023-05-08T18:47:08.967005ZWerkzeugDynamical fractional and multifractal fieldshttps://zbmath.org/1507.351612023-05-08T18:47:08.967005Z"Apolinário, Gabriel B."https://zbmath.org/authors/?q=ai:apolinario.gabriel-b"Chevillard, Laurent"https://zbmath.org/authors/?q=ai:chevillard.laurent"Mourrat, Jean-Christophe"https://zbmath.org/authors/?q=ai:mourrat.jean-christopheThe authors study a class of stochastic partial differential equations written as:
\[
\partial_{t}u_{H,\gamma ,\nu}=P_{H}\mathcal{L} P_{H}^{-1}u_{H,\gamma ,\nu}+\gamma P_{H}[P_{0}\mathcal{L} P_{H}^{-1}u_{H,\gamma ,\nu})(P_{H}^{-1}u_{H,\gamma ,\nu})]+\nu \partial_{x}^{2}u_{H,\gamma ,\nu}+f,
\]
where \(\mathcal{L}\) is the linear operator is defined as: \(\mathcal{L}u(t,x)\equiv 2i\pi cxu(t,x)\), \(c\) being a constant, \( P_{H}\) is the operator defined as: \(P_{H}u(t,x)=\int e^{2i\pi kx}\frac{1}{ \left\vert k\right\vert_{1/L}^{H+1/2}}\widehat{u}(t,k)dk\), \(\left\vert k\right\vert_{1/L}\) being a regularized absolute value over the wavelength \( 1/L\), such that \(\left\vert k\right\vert_{1/L}\approx \left\vert k\right\vert \), when \(\left\vert k\right\vert \gg 1/L\) and \(\left\vert k\right\vert_{1/L}\approx 1/L\) when \(\left\vert k\right\vert \ll 1/L\), \(\nu \geq 0\) is the fluid viscosity, \(f\) a random forcing term, which is supposed to be Gaussian, uncorrelated in time, statistically homogeneous, with zero average, and whose covariance is given as: \(\mathbb{E}[f(t,x)f^{\ast}(t,x)]=\delta (t-t^{\prime})C_{f}(x-x^{\prime})\), where \(^{\ast}\) stands for the complex conjugate, and \(C_{f}\) is a smooth function that decays rapidly away from the origin.
The authors first compute the statistical properties at large time of the solution \(u_{\nu}(t,x)\) to the partial differential equation: \(\partial_{t}u_{\nu}=\mathcal{L}u_{\nu}+\nu \partial_{x}^{2}u_{\nu}+f\), with and without the additional viscosity \( \nu \) and forcing term \(f\). They then prove that the solution to the equation: \(\partial_{t}u_{H,0}=P_{H}\mathcal{L}P_{H}^{-1}u_{H,0}+f\) goes as \(t\rightarrow \infty \) towards a statistically stationary regime for which they compute its finite variance and covariance. They finally prove a complex version of the Gaussian multiplicative chaos, considering the complex random field \(M_{\gamma}(t,x)=e^{\gamma v_{0}(t,x)}\), where \( v_{0}(t,x)=P_{0}u_{0}(t,x)\) is a fractional Gaussian field of parameter \(H=0\) , and they describe its asymptotic behavior as \(t\rightarrow \infty \). The paper ends with the presentation of a numerical scheme concerning the solution \(u_{H,\gamma ,\nu}\) and with an analysis of the numerical simulations.
Reviewer: Alain Brillard (Riedisheim)On the existence of weak solutions for an unsteady rotational Smagorinsky modelhttps://zbmath.org/1507.351642023-05-08T18:47:08.967005Z"Berselli, Luigi C."https://zbmath.org/authors/?q=ai:berselli.luigi-carlo"Kaltenbach, Alex"https://zbmath.org/authors/?q=ai:kaltenbach.alex"Růžička, M."https://zbmath.org/authors/?q=ai:ruzicka.michael"Lewandowski, Roger"https://zbmath.org/authors/?q=ai:lewandowski.rogerSummary: We show that the rotational Smagorinsky model for turbulent flows, can be put, for a wide range of parameters in the setting of Bochner pseudo-monotone evolution equations. This allows to prove existence of weak solutions a) identifying a proper functional setting in weighted spaces and b) checking some easily verifiable assumptions, at fixed time. We also will discuss the critical role of the exponents present in the model (power of the distance function and power of the curl) for what concerns the application of the theory of pseudo-monotone operators.Defects in liquid crystal flowshttps://zbmath.org/1507.351762023-05-08T18:47:08.967005Z"Gan, Zaihui"https://zbmath.org/authors/?q=ai:gan.zaihui"Hu, Xianpeng"https://zbmath.org/authors/?q=ai:hu.xianpeng"Lin, Fanghua"https://zbmath.org/authors/?q=ai:lin.fang-huaSummary: This paper concerns the dynamical properties of topological defects in two dimensional flows of liquid crystals modeled by the Ginzburg-Landau approximations. The fluid is transported by a nonlocal (an averaged) velocity and is coupled with effects of the elastic stress. The defects move along the trajectories of the flow associated with this averaged velocity, that is, \(\frac{d}{dt}a_j(t)={u}(a_j(t), t)\).Self-sustained oscillations of active viscoelastic matterhttps://zbmath.org/1507.760112023-05-08T18:47:08.967005Z"Plan, Emmanuel L. C. VI M."https://zbmath.org/authors/?q=ai:plan.emmanuel-lance-christopher-vi-medillo"Le Thi, Huong"https://zbmath.org/authors/?q=ai:le-thi.huong"Yeomans, Julia M."https://zbmath.org/authors/?q=ai:yeomans.julia-m"Doostmohammadi, Amin"https://zbmath.org/authors/?q=ai:doostmohammadi.aminSummary: Models of active nematics in biological systems normally require complexity arising from the hydrodynamics involved at the microscopic level as well as the viscoelastic nature of the system. Here we show that a minimal, space-independent, model based on the temporal alignment of active and polymeric particles provides an avenue to predict and study their coupled dynamics within the framework of dynamical systems. In particular, we examine, using analytical and numerical methods, how such a simple model can display self-sustained oscillations in an activity-driven viscoelastic shear flow.On wind-wave interaction phenomena at low Reynolds numbershttps://zbmath.org/1507.760512023-05-08T18:47:08.967005Z"Cimarelli, A."https://zbmath.org/authors/?q=ai:cimarelli.alessio|cimarelli.andrea"Romoli, F."https://zbmath.org/authors/?q=ai:romoli.f"Stalio, E."https://zbmath.org/authors/?q=ai:stalio.eSummary: After decades of research efforts, wind-wave interaction mechanisms have been recognized as extremely elusive. The reason is the complex nature of the problem, which combines complex coupling mechanisms between turbulent wind and water waves with the presence of multiple governing parameters, such as the friction Reynolds number of the wind, the water depth and the wind fetch. As shown unequivocally here, the use of suitable flow settings allows us to reduce the complex problem of wind-wave interaction to its essential features, mainly as a function of the sole friction Reynolds number of the wind. The resulting numerical solution allows us to study the interactions between water and air layers with their own fluid properties, and to unveil very interesting features, such as an oblique wave pattern travelling upstream and a wave-induced Stokes sublayer. The latter is responsible for a drag reduction mechanism in the turbulent wind. Despite the simulated flow conditions being far from the intense events occurring at the ocean-atmosphere interface, the basic flow phenomena unveiled here may explain some experimental evidence in wind-wave problems. Among other things, the wave-induced Stokes sublayer may shed light on the large scatter of the drag coefficient data in field measurements where swell waves of arbitrary directions are often present. Hence the present results and the developed approach pave the way for the understanding and modelling of the surface fluxes at the ocean-atmosphere interface, which are of overwhelming importance for climate science.Instability of a dusty Kolmogorov flowhttps://zbmath.org/1507.760562023-05-08T18:47:08.967005Z"Sozza, Alessandro"https://zbmath.org/authors/?q=ai:sozza.alessandro"Cencini, Massimo"https://zbmath.org/authors/?q=ai:cencini.massimo"Musacchio, Stefano"https://zbmath.org/authors/?q=ai:musacchio.stefano"Boffetta, Guido"https://zbmath.org/authors/?q=ai:boffetta.guidoSummary: Suspended particles can significantly alter the fluid properties and, in particular, can modify the transition from laminar to turbulent flow. We investigate the effect of heavy particle suspensions on the linear stability of the Kolmogorov flow by means of a multiple-scale expansion of the Eulerian model originally proposed by \textit{P. G. Saffman} [J. Fluid Mech. 13, 120--128 (1962; Zbl 0105.39605)]. We find that, while at small Stokes numbers particles always destabilize the flow (as already predicted by Saffman in the limit of very thin particles), at sufficiently large Stokes numbers the effect is non-monotonic in the particle mass fraction and particles can both stabilize and destabilize the flow. Numerical analysis is used to validate the analytical predictions. We find that in a region of the parameter space the multiple-scale expansion overestimates the stability of the flow and that this is a consequence of the breakdown of the scale separation assumptions.Numerical study of instabilities and compressibility effects on supersonic jet over a convex wallhttps://zbmath.org/1507.760672023-05-08T18:47:08.967005Z"Wang, Qing"https://zbmath.org/authors/?q=ai:wang.qing.5"Qu, Feng"https://zbmath.org/authors/?q=ai:qu.feng.1"Sun, Di"https://zbmath.org/authors/?q=ai:sun.di"Bai, Junqiang"https://zbmath.org/authors/?q=ai:bai.junqiangSummary: The supersonic jet over a convex wall is numerically investigated using the delayed detached-eddy simulation method based on the two-equation shear-stress transport model. The current study focuses on instabilities, turbulent statistics and the influence of compressibility effects. A widely applicable data-driven modal decomposition approach, called dynamic mode decomposition is used to gain further insight into the dynamical behaviours of the flow. The results demonstrate that streamwise vortices caused by the centrifugal force play significant roles in shear layer instabilities. The spanwise modulation of the streamwise vortices induces inflection points in the flow, resulting in secondary shear layer instability. This instability, which is sustained by the side-to-side sway of the streamwise vortices to obtain energy from the mean flow, dominates the rapid growth of the shear layer and turbulent stresses in the growth region. In the self-similar region, there is not only self-similarity of velocity profiles, but also self-similarity of normalized turbulent stresses. The compressibility effect significantly inhibits the growth of the shear layer and the formation of large-scale streamwise vortices. The investigation of turbulent stresses in the self-similar region with increasing convective Mach number indicates that the compressibility effect enhances turbulence anisotropy.Collapse of transitional wall turbulence captured using a rare events algorithmhttps://zbmath.org/1507.760702023-05-08T18:47:08.967005Z"Rolland, Joran"https://zbmath.org/authors/?q=ai:rolland.joranSummary: This text presents one of the first successful applications of a rare events sampling method for the study of multistability in a turbulent flow without stochastic energy injection. The trajectories of collapse of turbulence in plane Couette flow, and their probability and rate of occurrence are systematically computed using adaptive multilevel splitting (AMS). The AMS computations are performed in a system of size \(L_x\times L_z=24\times 18\) at Reynolds number \(R=370\) with an acceleration by a factor \(O(10)\) with respect to direct numerical simulations (DNS) and in a system of size \(L_x\times L_z=36\times 27\) at Reynolds number \(R=377\) with an acceleration by a factor \(O(10^3)\). The AMS results are validated by a comparison with DNS in the smaller system. Visualisations indicate that turbulence collapses because the self-sustaining process of turbulence fails locally. The streamwise vortices decay first in streamwise elongated holes, leaving streamwise invariant streamwise velocity tubes that experience viscous decay. These holes then extend in the spanwise direction. The examination of more than a thousand trajectories in the (\(E_{k,x}=\int u_x^2/2\,\mathrm{d}^3\boldsymbol{x}\), \(E_{k,y-z}=\int (u_y^2/2+u_z^2/2)\,\mathrm{d}^3\boldsymbol{x}\)) plane in the smaller system confirms the faster decay of streamwise vortices and shows concentration of trajectories. This hints at an instanton phenomenology in the large size limit. The computation of turning point states, beyond which laminarisation is certain, confirms the hole formation scenario and shows that it is more pronounced in larger systems. Finally, the examination of non-reactive trajectories indicates that both the vortices and the streaks reform concomitantly when the laminar holes close.Transitions in turbulent rotating Rayleigh-Bénard convectionhttps://zbmath.org/1507.760712023-05-08T18:47:08.967005Z"Schmitz, S."https://zbmath.org/authors/?q=ai:schmitz.s-w|schmitz.sylvain|schmitz.sebastian.2|schmitz.sabrina|schmitz.sven|schmitz.stephan|schmitz.stefan|schmitz.susanne"Tilgner, A."https://zbmath.org/authors/?q=ai:tilgner.andreasSummary: Numerical simulations of rotating Rayleigh-Bénard convection are presented for both no slip and free slip boundaries. The goal is to find a criterion distinguishing convective flows dominated by the Coriolis force from those nearly unaffected by rotation. If one uses heat transport as an indicator of which regime the flow is in, one finds that the transition between the flow regimes always occurs at the same value of a certain combination of Reynolds, Prandtl and Ekman numbers for both boundary conditions. If on the other hand one uses the helicity of the velocity field to identify flows nearly independent of rotation, one finds the transition at a different location in parameter space.Approach to the 4/3 law for turbulent pipe and channel flows examined through a reformulated scale-by-scale energy budgethttps://zbmath.org/1507.760722023-05-08T18:47:08.967005Z"Zimmerman, Spencer J."https://zbmath.org/authors/?q=ai:zimmerman.spencer-j"Antonia, R. A."https://zbmath.org/authors/?q=ai:antonia.robert-anthony"Djenidi, L."https://zbmath.org/authors/?q=ai:djenidi.lyazid"Philip, J."https://zbmath.org/authors/?q=ai:philip.jimmy"Klewicki, J. C."https://zbmath.org/authors/?q=ai:klewicki.joseph-cSummary: In this study, we propose a scale-by-scale (SBS) energy budget equation for flows with homogeneity in at least one direction. This SBS budget represents a modified form of the equation first proposed by \textit{L. Danaila} et al. [J. Fluid Mech. 430, 87--109 (2001; Zbl 0976.76030)] for the channel centreline -- the primary difference is that, here, we consider the role of pressure along with the errors associated with the isotropic approximations of the interscale divergence and Laplacian of the squared velocity increment. The term encompassing the effects of mean shear is also characterised such that the present analysis can be extended straightforwardly to locations away from the centreline. We show, based on a detailed analysis of previously published channel flow direct numerical simulations and pipe flow experiments near the centreline, how several terms in the present SBS budget equation (including the third-order velocity structure function) behave with increasing Reynolds number. The behaviour of these terms is shown to imply a rate of emergence and subsequent growth of the 4/3 law scale subrange at the channel centreline and pipe axis. The analysis also suggests that the peak magnitude of the third-order velocity structure function occurs at a scale that is fixed in proportion to the Taylor microscale at sufficiently high Reynolds number.The Batchelor-Howells-Townsend spectrum: three-dimensional casehttps://zbmath.org/1507.760732023-05-08T18:47:08.967005Z"Jolly, M. S."https://zbmath.org/authors/?q=ai:jolly.michael-summerfield"Wirosoetisno, D."https://zbmath.org/authors/?q=ai:wirosoetisno.djokoSummary: Given a velocity field \(u(x, t)\), we consider the evolution of a passive tracer \(\theta\) governed by \(\partial_t\theta + u\cdot\nabla\theta = \varDelta \theta + g\) with time-independent source \(g(x)\). When \(u\) is small in some sense, \textit{G. K. Batchelor} et al. [J. Fluid Mech. 5, 134--139 (1959; Zbl 0085.39702)] predicted that the tracer spectrum scales as \(|\theta_k|^2 \propto |k|^{-4} |u_k|^2\). Following our recent work for the two-dimensional case, in this paper we prove that the BHT59 scaling does hold probabilistically, asymptotically for large wavenumbers and for small enough random synthetic three-dimensional incompressible velocity fields \(u(x, t)\). We also relaxed some assumptions on the velocity and tracer source, allowing finite variances for both and full power spectrum for the latter.The influence of shear flow on the \(\alpha\)- and \(\gamma\)-effects in helical MHD turbulencehttps://zbmath.org/1507.760742023-05-08T18:47:08.967005Z"Leprovost, Nicolas"https://zbmath.org/authors/?q=ai:leprovost.nicolas"Kim, Eun-Jin"https://zbmath.org/authors/?q=ai:kim.eunjinSummary: We investigate the \(\alpha\)-effect and the turbulent transport of magnetic flux (\(\gamma\)-effect) by considering a turbulence driven by an isotropic helical forcing in the presence of a background large-scale shear flow. Due to shear flow, the turbulence is highly anisotropic. The effect of this shear-induced anisotropy on the structure of the electromotive force is computed self-consistently. We show that for weak shear, magnetic pumping (\(\gamma\)-effect) appears, and the \(\alpha\)-effect becomes highly anisotropic: the component of the \(\alpha\)-effect in the direction of the shear is smaller than the one in the direction perpendicular to the shear with non-vanishing non-diagonal components. However, a sufficiently strong shear leads to severe quenching of the \(\gamma\)- and \(\alpha\)-effects due to shear stabilisation.Diapycnal diffusivities in Kelvin-Helmholtz engendered turbulent mixing: the diffusive-convection regime in the arctic oceanhttps://zbmath.org/1507.760752023-05-08T18:47:08.967005Z"Ma, Yuchen"https://zbmath.org/authors/?q=ai:ma.yuchen"Peltier, W. R."https://zbmath.org/authors/?q=ai:peltier.w-rSummary: Recent progress in the direct measurement of turbulent dissipation in the Arctic Ocean has highlighted the need for an improved parametrization of the turbulent diapycnal diffusivities of heat and salt that is suitable for application in the turbulent environment characteristic of this polar region. In support of this goal we describe herein a series of direct numerical simulations of the turbulence generated in the process of growth and breaking of Kelvin-Helmholtz billows. These simulations provide the data sets needed to serve as basis for a study of the stratified turbulent mixing processes that are expected to exist in the Arctic Ocean environment. The mixing properties of the turbulence are studied using a previously formulated procedure in which the temperature and salinity fields are sorted separately in order to enable the separation of irreversible Arctic mixing from reversible stirring processes and thus the definition of turbulent diffusivities for both heat and salt that depend solely upon irreversible mixing. These analyses allow us to demonstrate that the irreversible diapycnal diffusivities for heat and salt are both solely dependent on the buoyancy Reynolds number in the Arctic Ocean environment. These are found to be in close agreement with the functional forms inferred for these turbulent diffusivities in the previous work of
\textit{D. Bouffard} and \textit{L. Boegman} [``A diapycnal diffusivity model for stratified environmental flows'', Dyn. Atmos. Oceans 61--62, 14--34 (2013; \url{doi:10.1016/j.dynatmoce.2013.02.002})]. Based on a detailed comparison of our simulation data with this previous empirical work, we propose an algorithm that can be used for inferring the diapycnal diffusivities from turbulent dissipation measurements in the Arctic Ocean.Turbulent mixed convection of heat in a greenhousehttps://zbmath.org/1507.760762023-05-08T18:47:08.967005Z"Kigo, James"https://zbmath.org/authors/?q=ai:kigo.james"Kinyanjui, Mathew"https://zbmath.org/authors/?q=ai:kinyanjui.mathew"Kiogora, Roy"https://zbmath.org/authors/?q=ai:kiogora.roy(no abstract)Residual-based closure model for density-stratified incompressible turbulent flowshttps://zbmath.org/1507.760772023-05-08T18:47:08.967005Z"Zhu, Lixing"https://zbmath.org/authors/?q=ai:zhu.lixing"Masud, Arif"https://zbmath.org/authors/?q=ai:masud.arifSummary: This paper presents a locally and dynamically adaptive residual-based closure model for density stratified incompressible flows. The method is based on the three-level form of the Variational Multiscale (VMS) modeling paradigm applied to the system of incompressible Navier-Stokes equations and an energy conservation equation for the relative temperature field. The velocity, pressure, and relative temperature fields are additively decomposed into overlapping scales which leads to a set of coupled mixed-field sub-problems for the coarse- and the fine-scales. In the hierarchical application of the VMS method, the fine-scale velocity and relative temperature fields are further decomposed, leading to a nested system of two-way coupled fine-scale level-I and level-II variational subproblems. A direct application of bubble functions approach to the fine-scale variational equations helps derive fine-scale models that are nonlinear and time dependent. Embedding the derived model from the level-II variational equation in the level-I variational equation helps stabilize the convection-dominated mixed-field thermodynamic subproblem. Locally resolving the unconstrained level-I variational equation yields the residual-based turbulence model which is a function of the residual of the Euler-Lagrange equations of the conservation of momentum, mass, and energy. The derived model accommodates forward- and back-scatter of energy and entropy and embeds sub-grid scale physics in the computable scales of the problem. The steps of the derivation show that it is essential to apply the concept of scale separation systematically to the coupled system of equations and it is critical to preserve the coupling between flow and thermal phases in the fine-scale variational equations. The method has been implemented with hexahedral and tetrahedral elements with equal order interpolations for the velocity, pressure, and temperature fields. Several canonical flow cases are presented that include Rayleigh-Bénard instability, Rayleigh-Taylor instability, and turbulent plane Couette flow with stable stratification.Assessment of turbulence models using DNS data of compressible plane free shear layer flowhttps://zbmath.org/1507.760782023-05-08T18:47:08.967005Z"Li, D."https://zbmath.org/authors/?q=ai:li.dongru"Komperda, J."https://zbmath.org/authors/?q=ai:komperda.jonathan"Peyvan, A."https://zbmath.org/authors/?q=ai:peyvan.ahmad"Ghiasi, Z."https://zbmath.org/authors/?q=ai:ghiasi.zia"Mashayek, F."https://zbmath.org/authors/?q=ai:mashayek.farzadSummary: The present paper uses the detailed flow data produced by direct numerical simulation (DNS) of a three-dimensional, spatially developing plane free shear layer to assess several commonly used turbulence models in compressible flows. The free shear layer is generated by two parallel streams separated by a splitter plate, with a naturally developing inflow condition. The DNS is conducted using a high-order discontinuous spectral element method (DSEM) for various convective Mach numbers. The DNS results are employed to provide insights into turbulence modelling. The analyses show that with the knowledge of the Reynolds velocity fluctuations and averages, the considered strong Reynolds analogy models can accurately predict temperature fluctuations and Favre velocity averages, while the extended strong Reynolds analogy models can correctly estimate the Favre velocity fluctuations and the Favre shear stress. The pressure-dilatation correlation and dilatational dissipation models overestimate the corresponding DNS results, especially with high compressibility. The pressure-strain correlation models perform excellently for most pressure-strain correlation components, while the compressibility modification model gives poor predictions. The results of an \textit{a priori} test for subgrid-scale (SGS) models are also reported. The scale similarity and gradient models, which are non-eddy viscosity models, can accurately reproduce SGS stresses in terms of structure and magnitude. The dynamic Smagorinsky model, an eddy viscosity model but based on the scale similarity concept, shows acceptable correlation coefficients between the DNS and modelled SGS stresses. Finally, the Smagorinsky model, a purely dissipative model, yields low correlation coefficients and unacceptable accumulated errors.Turbulent kinetic dissipation analysis for residual-based large eddy simulation of incompressible turbulent flow by variational multiscale methodhttps://zbmath.org/1507.760792023-05-08T18:47:08.967005Z"Chen, Linfeng"https://zbmath.org/authors/?q=ai:chen.linfeng"Hulshoff, Steven J."https://zbmath.org/authors/?q=ai:hulshoff.steven-j"Dong, Yuhong"https://zbmath.org/authors/?q=ai:dong.yuhongSummary: The underlying physical mechanism of the residual-based large eddy simulation (LES) based on the variational multiscale (VMS) method is clarified. Resolved large-scale energy transportation equation is mathematically derived for turbulent kinetic energy budget analysis. Firstly, statistical results of benchmark turbulent channel flow at \(R e_\tau = 180\) obtained using a coarse mesh are compared with the results obtained by the classical LES with the Smagorinsky and dynamic subgrid stress (SGS) model. The present LES shows an advantage in predicting the statistical results of the incompressible turbulent flows. Secondly, the contributions of the unresolved small-scale presentation terms (Term I--IV in Eq. (10)) to the turbulent kinetic dissipation are analysed for the VMS method. The results show that the turbulent kinetic dissipation provided by the numerical diffusion in the VMS method is smaller in the inner layer, larger in the outer layer of the channel flow than those by the Smagorinsky and dynamic SGS model. The turbulent kinetic dissipation in the VMS method is mainly given by the numerical diffusion provided by one of the ``cross-stress'' terms (Term I, same as the stabilization term in the SUPG method) and LSIC term (Term IV). The other one of the ``cross-stress'' terms (Term II) gives rise to the positive turbulent kinetic energy budget, and does not dissipate the turbulent kinetic energy. The so-called ``Reynolds stress'' term (Term III) dissipates the turbulent energy but provides a very small numerical diffusion. Finally, on the basis of the turbulent kinetic energy dissipation analysis, a new residual-based stabilized finite element formulation is proposed by modifying the large-scale equation in the VMS method. Numerical experiments of 2D lid-driven cavity flow and 3D incompressible turbulent channel flow are tested to validate the proposed formulation. It is shown that all the stabilization terms in the proposed formulation produce additional numerical diffusions and physically increase the total turbulent kinetic dissipation. Consequently, an apparent improvement in both the first-order and second-order statistical quantities are pursued by the new stabilized finite element formulation.Invariant data-driven subgrid stress modeling in the strain-rate eigenframe for large eddy simulationhttps://zbmath.org/1507.760802023-05-08T18:47:08.967005Z"Prakash, Aviral"https://zbmath.org/authors/?q=ai:prakash.aviral"Jansen, Kenneth E."https://zbmath.org/authors/?q=ai:jansen.kenneth-e"Evans, John A."https://zbmath.org/authors/?q=ai:evans.john-aSummary: We present a new approach for constructing data-driven subgrid stress models for large eddy simulation of turbulent flows. The key to our approach is representation of model input and output tensors in the filtered strain rate eigenframe. Provided inputs and outputs are selected and non-dimensionalized in a suitable manner, this yields a model form that is symmetric, Galilean invariant, rotationally invariant, reflectionally invariant, and unit invariant. We use this model form to train a simple and efficient neural network model using only one time step of filtered direct numerical simulation data from a forced homogeneous isotropic turbulence simulation. We demonstrate the accuracy of this model as well as the model's ability to generalize to previously unseen filter widths, Reynolds numbers, and flow physics using \textit{a priori} and \textit{a posteriori} tests.Reformulation and improvement of a universal subgrid eddy viscosity model based on the multiscale frameworkhttps://zbmath.org/1507.760812023-05-08T18:47:08.967005Z"Shui, Qingxiang"https://zbmath.org/authors/?q=ai:shui.qingxiang"Wu, Xinyi"https://zbmath.org/authors/?q=ai:wu.xinyi"Hong, Chao"https://zbmath.org/authors/?q=ai:hong.chao"Zhang, Yunwei"https://zbmath.org/authors/?q=ai:zhang.yunwei"Wong, Nyuk Hien"https://zbmath.org/authors/?q=ai:wong.nyuk-hien"Yu, Chuck Wah"https://zbmath.org/authors/?q=ai:yu.chuck-wah"Gu, Zhaolin"https://zbmath.org/authors/?q=ai:gu.zhaolin"Wang, Daguo"https://zbmath.org/authors/?q=ai:wang.daguoSummary: A universal multiscale Smagorinsky model (UMSM) is established for the large eddy simulation (LES) of wall-bounded turbulent flows by reformulating a universal subgrid eddy viscosity model presented by
\textit{Z. Gu} et al. [``The nature of a universal subgrid eddy viscosity model in a turbulent channel flow'', Europhys. Lett. 94, No. 3, Article ID 34003 (2011; \url{doi:10.1209/0295-5075/94/34003})].
The UMSM is adapted to the LES of wall-bounded turbulent flows by integrating the ``small-all'' form of the multiscale Smagorinsky model with the dynamic subgrid characteristic length, controlled by subgrid-scale (SGS) motions. The dynamic subgrid characteristic length is determined by the characteristic wave number, which is calculated from a new energy-weighted-mean method when the SGS turbulent kinetic energy and the dissipation wave number are known. The dissipation wave number is derived from the SGS turbulent kinetic energy spectrum equation and the total dissipation rate spectrum equation. The UMSM is used to simulate the fully developed channel flow and the turbulent flow past a square cylinder. The dynamic subgrid characteristic length, as a counterpart of Germano's procedure, evaluates the rapidly fluctuating small-scale behavior and spatial variations of turbulent characteristics. The results for fully developed channel flow show that the errors in the streamwise velocity and the velocity fluctuations change slowly. The flat nature of the UMSM error across different multiscale Smagorinsky coefficients (Cs') indicates that the model is relatively insensitive to the value of \(Cs'\). Additionally, the UMSM is less sensitive to grid resolution since more details of turbulence fluctuations are captured on the same grid-points compared to the
RVBMM
[\textit{U. Rasthofer} and \textit{V. Gravemeier}, J. Comput. Phys. 234, 79--107 (2013; Zbl 1284.76316)]
and
DSM
[\textit{C. Meneveau} et al., J. Fluid Mech. 319, 353--385 (1996; Zbl 0882.76029)].
Overall, the proposed model and the DSM exhibit similar behavior, and both LES formulations provide good agreement with reference data from direct numerical simulations. However, the UMSM is more computationally efficient, being 17\% faster than the dynamic Smagorinsky model.Unsteady flow prediction from sparse measurements by compressed sensing reduced order modelinghttps://zbmath.org/1507.760822023-05-08T18:47:08.967005Z"Zhang, Xinshuai"https://zbmath.org/authors/?q=ai:zhang.xinshuai"Ji, Tingwei"https://zbmath.org/authors/?q=ai:ji.tingwei"Xie, Fangfang"https://zbmath.org/authors/?q=ai:xie.fangfang"Zheng, Hongyu"https://zbmath.org/authors/?q=ai:zheng.hongyu"Zheng, Yao"https://zbmath.org/authors/?q=ai:zheng.yaoSummary: Prediction of complex fluid flows from sparse and noisy sensor measurements is widely applied to many engineering fields. In the present study, a novel compressed sensing reduced-order modeling framework has been proposed to predict unsteady flow fields from sparse and noisy sensor observations, which includes offline learning and online forecasting. In the offline learning stage, the Long Short Term Memory (LSTM) model is used for modeling the dynamic evolution of the sensor signals. Moreover, the sparsity-promoting Dynamic Mode Decomposition (DMD) algorithm is applied to extract spatio-temporal coherent structures from high-dimensional fluid dynamic system and choose optimal DMD modes for flow reconstruction. In order to establish the correlation between sensor space and feature-based coherent structures space, the Deep Neural Network (DNN) is employed. In the online forecasting stage, the trained framework is applied to predict the flow fields from limited sensor measurements in the actual experiment setup. In the current work, the proposed framework is applied in two numerical examples, including the flow past a circle cylinder at \(Re = 100\) characterized by laminar flow and at \(Re = 3900\) characterized by turbulent flow. It is shown that the proposed framework performs accurately and robustly in both prediction of sensor measurements and unsteady flow fields. Especially, the important physical features and quantities can be well maintained for both laminar and turbulent flow, even if high level noise is involved. Therefore, the proposed framework is a promising tool for sparse representation from complex flow fields in realistic experiments.Frame-independent vector-cloud neural network for nonlocal constitutive modeling on arbitrary gridshttps://zbmath.org/1507.760832023-05-08T18:47:08.967005Z"Zhou, Xu-Hui"https://zbmath.org/authors/?q=ai:zhou.xu-hui"Han, Jiequn"https://zbmath.org/authors/?q=ai:han.jiequn"Xiao, Heng"https://zbmath.org/authors/?q=ai:xiao.hengSummary: Constitutive models are widely used for modeling complex systems in science and engineering, where first-principle-based, well-resolved simulations are often prohibitively expensive. For example, in fluid dynamics, constitutive models are required to describe nonlocal, unresolved physics such as turbulence and laminar-turbulent transition. However, traditional constitutive models based on partial differential equations (PDEs) often lack robustness and are too rigid to accommodate diverse calibration datasets. We propose a frame-independent, nonlocal constitutive model based on a vector-cloud neural network that can be learned with data. The model predicts the closure variable at a point based on the flow information in its neighborhood. Such nonlocal information is represented by a group of points, each having a feature vector attached to it, and thus the input is referred to as vector cloud. The cloud is mapped to the closure variable through a frame-independent neural network, invariant both to coordinate translation and rotation and to the ordering of points in the cloud. As such, the network can deal with any number of arbitrarily arranged grid points and thus is suitable for unstructured meshes in fluid simulations. The merits of the proposed network are demonstrated for scalar transport PDEs on a family of parameterized periodic hill geometries. The vector-cloud neural network is a promising tool not only as nonlocal constitutive models and but also as general surrogate models for PDEs on irregular domains.Stochastic modelling of unresolved eddy fluxeshttps://zbmath.org/1507.760842023-05-08T18:47:08.967005Z"Zidikheri, Meelis J."https://zbmath.org/authors/?q=ai:zidikheri.meelis-juma"Frederiksen, Jorgen S."https://zbmath.org/authors/?q=ai:frederiksen.jorgen-segerlundSummary: A subgrid-scale parameterization scheme motivated by statistical closure theory, but employing statistics obtained from high-resolution direct numerical simulations, is applied to large eddy simulations of two-level quasigeostrophic turbulence on the sphere. It is shown that these parameterizations are consistent with the phenomenology of quasigeostrophic turbulence. The parameterizations consist of \(2 \times 2\) dissipation and stochastic forcing covariance matrices at each wavenumber, with the off-diagonal elements of the matrices representing vertical mixing. Two flow regimes, characterized by their deformation scales, are considered, namely atmospheric and oceanic. In the former, the deformation scale is fully resolved, and the truncation scale is within the enstrophy cascading interial range. In the latter, the deformation scale is not fully resolved, and the truncation scale is within the energy cascading inertial range. It is demonstrated through numerical experiments that both stochastic and deterministic variants of the scheme give comparable results for the energy spectra in the atmospheric regime. In the oceanic regime, the stochastic variant again gives excellent results, but the deterministic variant is found to be numerically unstable.Identifying the multifractal set on which energy dissipates in a turbulent Navier-Stokes fluidhttps://zbmath.org/1507.760852023-05-08T18:47:08.967005Z"Gibbon, John D."https://zbmath.org/authors/?q=ai:gibbon.john-dSummary: The rich multifractal properties of fluid turbulence illustrated by the work of \textit{U. Frisch} and \textit{G. Parisi} [``Appendix: On the singularity structure of fully developed turbulence'', in: M. Ghil (ed.) et al., Turbulence and predictability in geophysical fluid dynamics. Amsterdam: North Holland. 84--87 (1985)] are related explicitly to Leray's weak solutions of the three-dimensional Navier-Stokes equations. Directly from this correspondence it is found that the set on which energy dissipates, \(\mathbb{F}_m\), has a range of dimensions \(\mathfrak{D}_m = 3/m\) (\(1 \leq m \leq \infty\)), and a corresponding range of sub-Kolmogorov dissipation inverse length scales \(L\eta_m^{-1} \leq Re^{3/(1 + \mathfrak{D}_m)}\) spanning \(Re^{3/4}\) to \(Re^3\). Correspondingly, the multifractal model scaling parameter \(h\), must obey \(h \geq h_{min}\) with \(-\frac{2}{3} \leq h_{min} \leq \frac{1}{3}\).An efficient discretization for a family of time relaxation modelshttps://zbmath.org/1507.760942023-05-08T18:47:08.967005Z"Belding, Jeffrey"https://zbmath.org/authors/?q=ai:belding.jeffrey"Neda, Monika"https://zbmath.org/authors/?q=ai:neda.monika"Lan, Rihui"https://zbmath.org/authors/?q=ai:lan.rihuiSummary: In this paper, we present a finite element study for the family of Time Relaxation models using the recently proposed EMAC discretization of the non-linear term. This discretization conserves energy, momentum and angular momentum. We study the conservation properties, stability and error estimates in the fully discrete case. Comparisons with the classical skew symmetric non-linear formulation are drawn throughout the paper. We will show that the error estimate for EMAC is improved over the skew symmetric scheme based on the constant obtained from the application of Gronwall's inequality. Numerical experiments in 2D and 3D showing the advantage of EMAC over skew symmetric are performed as well.Gradient jump penalty stabilisation of spectral/\( h p\) element discretisation for under-resolved turbulence simulationshttps://zbmath.org/1507.761182023-05-08T18:47:08.967005Z"Moura, Rodrigo C."https://zbmath.org/authors/?q=ai:moura.rodrigo-costa"Cassinelli, Andrea"https://zbmath.org/authors/?q=ai:cassinelli.andrea"da Silva, André F. C."https://zbmath.org/authors/?q=ai:da-silva.andre-f-c"Burman, Erik"https://zbmath.org/authors/?q=ai:burman.erik"Sherwin, Spencer J."https://zbmath.org/authors/?q=ai:sherwin.spencer-jSummary: One of the strengths of the discontinuous Galerkin (DG) method has been its balance between accuracy and robustness, which stems from DG's intrinsic (upwind) dissipation being biased towards high frequencies/wavenumbers. This is particularly useful in high Reynolds-number flow simulations where limitations on mesh resolution typically lead to potentially unstable under-resolved scales. In continuous Galerkin (CG) discretisations, similar properties are achievable through the addition of artificial diffusion such as spectral vanishing viscosity (SVV). However although SVV is recognised as very useful in CG-based high-fidelity turbulence simulations, this approach has been observed to be sub-optimal when compared to DG at intermediate polynomials orders \(( P \approx 3)\). In this paper we explore an alternative stabilisation approach through the introduction of a continuous interior penalty on the gradient discontinuity at elemental boundaries, which we refer to as a gradient jump penalisation (GJP). Analogous to DG methods, this introduces a penalisation at the elemental interfaces as opposed to the interior element stabilisation of SVV. Detailed eigenanalysis of the GJP approach shows its potential as equivalent (sometimes superior) to DG dissipation and hence superior to previous SVV approaches. Through eigenanalysis, a judicious choice of GJP's \(P\)-dependent scaling parameter is made and found to be consistent with previous a-priori error analysis. The favourable properties of the GJP stabilisation approach are also supported by turbulent flow simulations of the incompressible Navier-Stokes equation, as we achieve higher quality flow solutions at \(P = 3\) using GJP, whereas SVV performs marginally worse at \(P = 5\) with twice as many degrees of freedom in total.Effective implementation of the parallel SIMPLE algorithm based on multigrid methodhttps://zbmath.org/1507.761372023-05-08T18:47:08.967005Z"Kozelkov, A. S."https://zbmath.org/authors/?q=ai:kozelkov.andrey-sergeevich"Lashkin, S. V."https://zbmath.org/authors/?q=ai:lashkin.sergey-victorovich"Kurkin, A. A."https://zbmath.org/authors/?q=ai:kurkin.andrei-aleksandrovich"Kornev, A. V."https://zbmath.org/authors/?q=ai:kornev.a-v"Vyalykh, A. M."https://zbmath.org/authors/?q=ai:vyalykh.a-m(no abstract)Finite volume models and efficient simulation tools (EST) for shallow flowshttps://zbmath.org/1507.761402023-05-08T18:47:08.967005Z"Martínez-Aranda, S."https://zbmath.org/authors/?q=ai:martinez-aranda.s"Fernández-Pato, J."https://zbmath.org/authors/?q=ai:fernandez-pato.j"Echeverribar, I."https://zbmath.org/authors/?q=ai:echeverribar.i"Navas-Montilla, A."https://zbmath.org/authors/?q=ai:navas-montilla.a"Morales-Hernández, M."https://zbmath.org/authors/?q=ai:morales-hernandez.m-d|morales-hernandez.monica"Brufau, P."https://zbmath.org/authors/?q=ai:brufau.pilar"Murillo, J."https://zbmath.org/authors/?q=ai:murillo.javier"García-Navarro, P."https://zbmath.org/authors/?q=ai:garcia-navarro.pilarSummary: Shallow-type mathematical models are built in the context of free surface flows over the main hypothesis that the flow layer depth is smaller than a relevant horizontal length scale. There is a wide range of physical situations in which these shallow-type formulations are applicable, such as open channels and rivers, tsunamis, floods, landslides or muddy slurries. Their numerical solution on the finite volume framework is governed by the dynamical properties of the flow, the uneven distribution of the bed level and also by the computational grid choice. The unified discretization of spatial flux derivatives and source terms has proven useful to ensure the properties of monotonicity, stability and conservation in the numerical solution. Surface shallow flows that occur in catchments and coasts usually require large space resolution over longer periods of time. The increasing complexity of the mathematical models, the advancements in numerical methods, as well as the increasing power of computation are making possible the physically-based simulation of these phenomena. The necessity of spatial resolution involves the use of a large number of elements, which increases the computational time when simulating realistic scenarios for a long time period. The resulting approach from the proper mathematical formulation, robust numerical resolution and efficient computational implementation of models (EST) can be very useful in the simulation of environmental surface processes with realistic temporal and spatial scales.
For the entire collection see [Zbl 1487.76005].Output-based error estimation and mesh adaptation for unsteady turbulent flow simulationshttps://zbmath.org/1507.761802023-05-08T18:47:08.967005Z"Fidkowski, Krzysztof J."https://zbmath.org/authors/?q=ai:fidkowski.krzysztof-jSummary: This paper presents a method for estimating output errors and adapting computational meshes in simulations of unsteady turbulent flows. The chaotic nature of such problems prevents a stable unsteady adjoint solution, and existing regularization techniques are costly for large simulations. The method presented foregoes the unsteady adjoint and instead relies on a field-inversion machine-learning (FIML) framework, which only requires unsteady primal solutions without full-state storage or checkpointing. The FIML model yields an adjoint for the averaged solution, which is combined with an averaged unsteady residual to obtain an output error estimate and adaptive indicator. This error estimate is shown to be accurate when the FIML model augments the original unsteady equations with corrections that are not excessively large. The unsteady residual comes from sampling fine-space residual evaluations during the unsteady simulation. A novel objective function based on an adjoint-weighted residual is presented for the field inversion to improve the ability of the FIML model to predict output errors and the domain-interior state. The localized output error drives adaptation of the mesh size and approximation order. Results for three aerodynamic problems ranging in Reynolds number demonstrate accuracy of the error estimates and efficiency of the computational meshes when compared to other adaptive strategies, including uniform and residual-based refinement.Thermohaline staircase formation in the diffusive convection regime: a theory based upon stratified turbulence asymptoticshttps://zbmath.org/1507.761922023-05-08T18:47:08.967005Z"Ma, Yuchen"https://zbmath.org/authors/?q=ai:ma.yuchen"Peltier, W. R."https://zbmath.org/authors/?q=ai:peltier.w-rSummary: We describe a mechanism that leads to the spontaneous formation of a thermohaline staircase in the high-latitude oceans. Our analysis of this mechanism is based upon a model in which uniform gradients of temperature and salinity are assumed and is applied to a simplified mean-field model of stratified turbulence. Detailed analysis employs a parametrization of turbulent diapycnal diffusivities [\textit{D. Bouffard} and \textit{L. Boegman}, ``A diapycnal diffusivity model for stratified environmental flows'', Dyn. Atmos. Oceans 61--62, 14--34 (2013; \url{doi:10.1016/j.dynatmoce.2013.02.002})]. This parametrization is apparently unique in that it distinguishes between the diapycnal diffusivities for heat and salt on the basis of their Prandtl (Schmidt) numbers. Our model predicts that the temperature and salinity profiles will be susceptible to linear instability if the buoyancy Reynolds number lies in the range 0.18--91, and a nonlinear mean-field model simulation demonstrates that it evolves into a well-defined thermohaline staircase that matches the characteristics of those found in the high-latitude oceans. The criterion for initial instability is furthermore shown to be consistent with the observed regional variability of staircase occurrence in the Arctic Ocean as determined by the most recent observational datasets.NS-\(\omega\) model for fluid-fluid interaction problems at high Reynolds numbershttps://zbmath.org/1507.762302023-05-08T18:47:08.967005Z"Aggul, Mustafa"https://zbmath.org/authors/?q=ai:aggul.mustafa"Labovsky, Alexander E."https://zbmath.org/authors/?q=ai:labovsky.alexander-e"Schwiebert, Kyle J."https://zbmath.org/authors/?q=ai:schwiebert.kyle-jSummary: We consider a fluid-fluid interaction problem, where two flows are coupled through a nonlinear rigid lid condition, and one or both of these flows are at high Reynolds numbers. A method is proposed, that combines the NS-\(\omega\) turbulence model with a partitioning method -- so that the resulting model is efficiently decoupled, allows for the usage of preexisting solvers (e.g., air and water domain solvers), and is capable of resolving the flows at high Reynolds numbers. The model is shown to be unconditionally stable and have optimal convergence properties. The model also allows for the non-filtered velocity in the interface terms; it has been shown recently that filtering the velocity in the interface terms could corrupt the quality of the model's solution. To the best of the authors' knowledge, this is the first model with non-filtered velocity on the interface, that lends itself to full numerical analysis.The dynamics of unforced turbulence at high Reynolds number for Taylor-Green vortices generalized to MHDhttps://zbmath.org/1507.762512023-05-08T18:47:08.967005Z"Pouquet, A."https://zbmath.org/authors/?q=ai:pouquet.annick-g"Lee, E."https://zbmath.org/authors/?q=ai:lee.eunjeong|lee.euiwoong|lee.euntaek|lee.eunjee|lee.euikyoo|lee.eunsoo|lee.eugene|lee.eunkyu|lee.eunkyoung|lee.ela|lee.eunsung|lee.eunseok|lee.eunjin|lee.eungu|lee.eonkyung|lee.eungjun|lee.eungki|lee.eunhee|lee.eunjung|lee.erick|lee.eunju|lee.eunjoo|lee.eunjae|lee.edmund|lee.eojin|lee.eunsang|lee.euncheol|lee.euiwoo|lee.eysa"Brachet, M. E."https://zbmath.org/authors/?q=ai:brachet.marc-etienne"Mininni, P. D."https://zbmath.org/authors/?q=ai:mininni.pablo-d"Rosenberg, D."https://zbmath.org/authors/?q=ai:rosenberg.duaneSummary: We study decaying magnetohydrodynamics (MHD) turbulence stemming from the evolution of the Taylor-Green flow generalized recently to MHD, with equal viscosity and magnetic resistivity and up to equivalent grid resolutions of \(2048^3\) points. A pseudo-spectral code is used in which the symmetries of the velocity and magnetic fields have been implemented, allowing for sizable savings in both computer time and usage of memory at a given Reynolds number. The flow is non-helical, and at initial time the kinetic and magnetic energies are taken to be equal and concentrated in the large scales. After testing the validity of the method on grids of \(512^3\) points, we analyze the data on the large grids up to Taylor Reynolds numbers of \(\approx 2200\). We find that the global temporal evolution is accelerated in MHD, compared to the corresponding neutral fluid case. We also observe an interval of time when such configurations have quasi-constant total dissipation, time during which statistical properties are determined after averaging over of the order of two turn-over times. A weak turbulence spectrum is obtained which is also given in terms of its anisotropic components. Finally, we contrast the development of small-scale eddies with two other initial conditions for the magnetic field and briefly discuss the structures that develop, and which display a complex array of current and vorticity sheets with clear rolling-up and folding.Large-scale fluctuations and dynamics of the bullard-von Kármán dynamohttps://zbmath.org/1507.762552023-05-08T18:47:08.967005Z"Verhille, Gautier"https://zbmath.org/authors/?q=ai:verhille.gautier"Plihon, Nicolas"https://zbmath.org/authors/?q=ai:plihon.nicolas"Fanjat, Grégory"https://zbmath.org/authors/?q=ai:fanjat.gregory"Volk, Romain"https://zbmath.org/authors/?q=ai:volk.romain"Bourgoin, Mickael"https://zbmath.org/authors/?q=ai:bourgoin.mickael"Pinton, Jean-François"https://zbmath.org/authors/?q=ai:pinton.jean-francoisSummary: A synthetic fluid dynamo built in the spirit of the Bullard device [\textit{E. C. Bullard}, The stability of a homopolar dynamo. Proc. Camb. Phil. Soc. 51, No. 4, 744--760 (1955; \url{doi:10.1017/S0305004100030814})] is investigated. It is a two-step dynamo in which one process stems from the fluid turbulence, while the other part is achieved by a linear amplification of currents in external coils [\textit{M. Bourgoin} et al., A Bullard-von Kármán dynamo, New J. Phys. 8, 329 (2006; \url{doi:10.1088/1367-2630/8/12/329})]. Modifications in the forcing are introduced in order to change the dynamics of the flow, and hence the dynamo behavior. Some features, such as on-off intermittency at onset of dynamo action, are very robust. Large-scale fluctuations have a significant impact on the resulting dynamo, in particular in the observation of magnetic field reversals.A multiscale approach for the study of particle-laden flows using a continuous modelhttps://zbmath.org/1507.762612023-05-08T18:47:08.967005Z"Idelsohn, Sergio R."https://zbmath.org/authors/?q=ai:idelsohn.sergio-rodolfo"Gimenez, Juan M."https://zbmath.org/authors/?q=ai:gimenez.juan-marcelo"Löhner, Rainald"https://zbmath.org/authors/?q=ai:lohner.rainald"Oñate, Eugenio"https://zbmath.org/authors/?q=ai:onate.eugenioSummary: The methodology previously proposed by the authors to solve particle-laden turbulent flows through a multiscale approach is extended by introducing a continuous function for the dispersed phase concentration. The proposed continuous model is especially useful for studying the motion of particle streams in which gravitational and inertial effects cause the particles to deviate from a simple trajectory following the surrounding flow, as would be the case for the limit of very small, massless particles. The results show an excellent comparison between the solutions obtained using the continuous model and simulations evaluating the forces on each particle individually. Distinct advantages of the continuous approach are a much lower computational overhead, a better load balance and ease of parallelization. The multiscale methodology proposed may be used in the area of modeling and simulation of airborne infectious diseases.The gauge invariant cosmological Jacobi map from weak lensing at leading orderhttps://zbmath.org/1507.830212023-05-08T18:47:08.967005Z"Fanizza, Giuseppe"https://zbmath.org/authors/?q=ai:fanizza.giuseppe"Di Dio, Enea"https://zbmath.org/authors/?q=ai:di-dio.enea"Durrer, Ruth"https://zbmath.org/authors/?q=ai:durrer.ruth"Marozzi, Giovanni"https://zbmath.org/authors/?q=ai:marozzi.giovanni(no abstract)Magnetic helicity fluxes in an \(\alpha^2\) dynamo embedded in a halohttps://zbmath.org/1507.850202023-05-08T18:47:08.967005Z"Hubbard, Alexander"https://zbmath.org/authors/?q=ai:hubbard.alexander"Brandenburg, Axel"https://zbmath.org/authors/?q=ai:brandenburg.axelSummary: We present the results of simulations of forced turbulence in a slab where the mean kinetic helicity has a maximum near the mid-plane, generating gradients of magnetic helicity of both large and small-scale fields. We also study systems that have poorly conducting buffer zones away from the midplane in order to assess the effects of boundaries. The dynamical \(\alpha\) quenching phenomenology requires that the magnetic helicity in the small-scale fields approaches a nearly static, gauge independent state. To stress-test this steady state condition we choose a system with a uniform sign of kinetic helicity, so that the total magnetic helicity can reach a steady state value only through fluxes through the boundary, which are themselves suppressed by the velocity boundary conditions. Even with such a set up, the small-scale magnetic helicity is found to reach a steady state. In agreement with the earlier work, the magnetic helicity fluxes of small-scale fields are found to be turbulently diffusive. By comparing results with and without halos, we show that artificial constraints on magnetic helicity at the boundary do not have a significant impact on the evolution of the magnetic helicity, except that ``softer'' (halo) boundary conditions give a lower energy of the saturated mean magnetic field.