Robust numerical schemes for anisotropic diffusion problems, a first step for turbulence modeling in Lagrangian hydrodynamics
Numerous systems of conservation laws are discretized on Lagrangian meshes where cells nodes move with matter. For complex applications, cells shape or aspect ratio often do not insure sufficient accuracy to provide an acceptable numerical solution and use of ALE technics is necessary. Here we are i...
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Published in | ESAIM. Proceedings Vol. 28; pp. 80 - 99 |
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Main Authors | , , , , , , |
Format | Journal Article |
Language | English |
Published |
EDP Sciences
23.11.2009
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Series | CEMRACS 2008 - Modelling and Numerical Simulation of Complex Fluids |
Subjects | |
Online Access | Get full text |
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Abstract | Numerous systems of conservation laws are discretized on Lagrangian meshes where cells nodes move with matter. For complex applications, cells shape or aspect ratio often do not insure sufficient accuracy to provide an acceptable numerical solution and use of ALE technics is necessary. Here we are interested with conduction phenomena depending on velocity derivatives coming from the resolution of gas dynamics equations. For that, we propose the study of a mock of second order turbulent mixing model combining an elliptical part and an hyperbolic kernel. The hyperbolic part is approximated by finite-volume centered scheme completed by a remapping step see [7]. A major part of this paper is the discretization of the anisotropic parabolic equation on polygonal distorted mesh. It is based on the scheme described in [9] ensuring the positivity of the numerical solution. We propose an alternative based on the partitioning of polygons in triangles. We show some preliminary results on a weak coupling of hydrodynamics and parabolic equation whose tensor diffusion coefficient depends on Reynolds stresses.
De nombreux systèmes de lois de conservation sont intégrés à l'aide du formalisme lagrangien où les sommets des mailles voient leurs position varier au cours du temps. La forme des mailles ne permet pas toujours d'assurer une bonne précision du calcul et les techniques ALE sont nécessaires. Nous nous intéressons ici à des phénomènes de conduction dépendant du gradient de vitesse couplés à la dynamique des gaz. Pour cela, nous proposons l'étude d'un simulacre de modèle de mélange turbulent du second ordre construit pour combiner terme elliptique et noyau hyperbolique. La partie hyperbolique est résolue par des schéma centrés volumes-finis et le remaillage de la phase ALE est celui décrit dans [7]. Une partie importante de ce papier est la discrétisation de l'équation parabolique anisotrope sur maillage polygonal non régulier. Celle-ci s'inspire du schéma dans [9] qui assure la positivité de la solution numérique. Nous proposons une variante basée sur le découpage en triangles des mailles polygonales. Nous montrons quelques résultats préliminaires sur un couplage faible hydrodynamique et équation parabolique dont le tenseur de diffusion dépend des tensions de Reynolds. |
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AbstractList | Numerous systems of conservation laws are discretized on Lagrangian meshes where cells nodes move with matter. For complex applications, cells shape or aspect ratio often do not insure sufficient accuracy to provide an acceptable numerical solution and use of ALE technics is necessary. Here we are interested with conduction phenomena depending on velocity derivatives coming from the resolution of gas dynamics equations. For that, we propose the study of a mock of second order turbulent mixing model combining an elliptical part and an hyperbolic kernel. The hyperbolic part is approximated by finite-volume centered scheme completed by a remapping step see [7]. A major part of this paper is the discretization of the anisotropic parabolic equation on polygonal distorted mesh. It is based on the scheme described in [9] ensuring the positivity of the numerical solution. We propose an alternative based on the partitioning of polygons in triangles. We show some preliminary results on a weak coupling of hydrodynamics and parabolic equation whose tensor diffusion coefficient depends on Reynolds stresses.
De nombreux systèmes de lois de conservation sont intégrés à l'aide du formalisme lagrangien où les sommets des mailles voient leurs position varier au cours du temps. La forme des mailles ne permet pas toujours d'assurer une bonne précision du calcul et les techniques ALE sont nécessaires. Nous nous intéressons ici à des phénomènes de conduction dépendant du gradient de vitesse couplés à la dynamique des gaz. Pour cela, nous proposons l'étude d'un simulacre de modèle de mélange turbulent du second ordre construit pour combiner terme elliptique et noyau hyperbolique. La partie hyperbolique est résolue par des schéma centrés volumes-finis et le remaillage de la phase ALE est celui décrit dans [7]. Une partie importante de ce papier est la discrétisation de l'équation parabolique anisotrope sur maillage polygonal non régulier. Celle-ci s'inspire du schéma dans [9] qui assure la positivité de la solution numérique. Nous proposons une variante basée sur le découpage en triangles des mailles polygonales. Nous montrons quelques résultats préliminaires sur un couplage faible hydrodynamique et équation parabolique dont le tenseur de diffusion dépend des tensions de Reynolds. |
Author | Kuate, Raphaël Rebourcet, Bernard Weynans, Lisl Dambrine, Julien Lohéac, Jérôme Hoch, Philippe Métral, Jérôme |
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Title | Robust numerical schemes for anisotropic diffusion problems, a first step for turbulence modeling in Lagrangian hydrodynamics |
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