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A finite volume scheme for solving anisotropic diffusion on ALE‐AMR grids
Author(s) -
Breil Jérôme,
Jacq Pascal,
Maire PierreHenri
Publication year - 2017
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4368
Subject(s) - finite volume method , polygon mesh , robustness (evolution) , eulerian path , grid , mathematics , adaptive mesh refinement , anisotropic diffusion , mesh generation , numerical diffusion , regularization (linguistics) , computer science , anisotropy , finite element method , mathematical optimization , lagrangian , physics , mechanics , computational science , geometry , biochemistry , chemistry , quantum mechanics , artificial intelligence , gene , thermodynamics
Summary In the context of High Energy Density Physics and more precisely in the field of laser plasma interaction, Lagrangian schemes are commonly used. The lack of robustness due to strong grid deformations requires the regularization of the mesh through the use of Arbitrary Lagrangian Eulerian methods. Theses methods usually add some diffusion and a loss of precision is observed. We propose to use Adaptive Mesh Refinement (AMR) techniques to reduce this loss of accuracy. This work focuses on the resolution of the anisotropic diffusion operator on Arbitrary Lagrangian Eulerian‐AMR grids. In this paper, we describe a second‐order accurate cell‐centered finite volume method for solving anisotropic diffusion on AMR type grids. The scheme described here is based on local flux approximation which can be derived through the use of a finite difference approximation, leading to the CCLADNS scheme. We present here the 2D and 3D extension of the CCLADNS scheme to AMR meshes. Copyright © 2017 John Wiley & Sons, Ltd.