[Un schéma à neuf points pour la diffusion en milieu hétérogène]
Nous proposons un schéma ayant ses inconnues aux centres des mailles, combinant les avantages des schémas à flux multi-points et des schémas hybrides : il possède un stencil à 9 points en 2D, respecte les hétérogénéités de la matrice de diffusion, et il est coercif ; de plus, on peut montrer qu'il converge. Le schéma est basé sur l'utilisation de points situé aux interfaces d'hétérogénéité, en lesquels la formule de la moyenne harmonique est utilisable.
We propose a cell-centered symmetric scheme which combines the advantages of MPFA (multipoint flux approximation) schemes such as the L or the O scheme and of hybrid schemes: it may be used on general non-conforming meshes, it yields a 9-point stencil on two-dimensional quadrangular meshes, it takes into account the heterogeneous diffusion matrix, it is coercive and it can be shown to converge. The scheme relies on the use of special points, called harmonic averaging points, located at the interfaces of heterogeneity.
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@article{CRMATH_2009__347_11-12_673_0,
author = {Agelas, L\'eo and Eymard, Robert and Herbin, Rapha\`ele},
title = {A nine-point finite volume scheme for the simulation of diffusion in heterogeneous media},
journal = {Comptes Rendus. Math\'ematique},
pages = {673--676},
publisher = {Elsevier},
volume = {347},
number = {11-12},
year = {2009},
doi = {10.1016/j.crma.2009.03.013},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2009.03.013/}
}
TY - JOUR AU - Agelas, Léo AU - Eymard, Robert AU - Herbin, Raphaèle TI - A nine-point finite volume scheme for the simulation of diffusion in heterogeneous media JO - Comptes Rendus. Mathématique PY - 2009 SP - 673 EP - 676 VL - 347 IS - 11-12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.03.013/ DO - 10.1016/j.crma.2009.03.013 LA - en ID - CRMATH_2009__347_11-12_673_0 ER -
%0 Journal Article %A Agelas, Léo %A Eymard, Robert %A Herbin, Raphaèle %T A nine-point finite volume scheme for the simulation of diffusion in heterogeneous media %J Comptes Rendus. Mathématique %D 2009 %P 673-676 %V 347 %N 11-12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.03.013/ %R 10.1016/j.crma.2009.03.013 %G en %F CRMATH_2009__347_11-12_673_0
Agelas, Léo; Eymard, Robert; Herbin, Raphaèle. A nine-point finite volume scheme for the simulation of diffusion in heterogeneous media. Comptes Rendus. Mathématique, Tome 347 (2009) no. 11-12, pp. 673-676. doi : 10.1016/j.crma.2009.03.013. http://www.numdam.org/articles/10.1016/j.crma.2009.03.013/
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☆ Work supported by Groupement de Recherche MOMAS, PACEN/CNRS.
