Schéma volumes finis pour des opérateurs de diffusion fortement anisotropes sur des maillages non structurés

Christophe Le Potier

doi:10.1016/j.crma.2005.05.011

Analyse numérique

Schéma volumes finis pour des opérateurs de diffusion fortement anisotropes sur des maillages non structurés

Présenté par : Philippe G. Ciarlet

Christophe Le Potier ¹

¹ Commissariat à l'énergie atomique, DEN/DM2S/SFME/MTMS, 91191 Gif-sur-Yvette cedex, France

Comptes Rendus. Mathématique, Volume 340 (2005) no. 12, pp. 921-926.

Résumé
Abstract

Nous décrivons une méthode de volumes finis pour des opérateurs de diffusion fortement anisotropes sur des maillages déformés. L'idée principale est de calculer le gradient sur chaque noeud de chaque maille à l'aide de l'inconnue principale au centre des mailles et d'inconnues auxiliaires définies sur les arêtes du maillage. Ces dernières sont éliminées en imposant des relations de continuité des flux. La matrice globale associée à ce schéma est symétrique définie positive. Nous montrons la robustesse et la précision de la méthode par comparaison à des solutions analytiques et aux résultats obtenus par d'autres schémas numériques.

We introduce a finite volume method for highly anisotropic diffusion operators on unstructured meshes. The main idea is to calculate the gradient on each cell vertex using the cell-centered unknown and other unknowns calculated on the cell edges. These degrees of freedom are eliminated imposing flux continuity conditions. The resulting global matrix is symmetric and positive definite. We show the robustness and the precision of the method in comparison with analytical solutions and results obtained by other numerical schemes.

Reçu le : 2004-10-26
Accepté le : 2005-05-19
Publié le : 2005-06-15

DOI : 10.1016/j.crma.2005.05.011

Affiliations des auteurs :

Christophe Le Potier ¹

¹ Commissariat à l'énergie atomique, DEN/DM2S/SFME/MTMS, 91191 Gif-sur-Yvette cedex, France

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     journal = {Comptes Rendus. Math\'ematique},
     pages = {921--926},
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     doi = {10.1016/j.crma.2005.05.011},
     language = {fr},
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Christophe Le Potier. Schéma volumes finis pour des opérateurs de diffusion fortement anisotropes sur des maillages non structurés. Comptes Rendus. Mathématique, Volume 340 (2005) no. 12, pp. 921-926. doi : 10.1016/j.crma.2005.05.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.05.011/

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