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Comptes Rendus Mathématique
Volume 341, n° 12
pages 787-792 (décembre 2005)
Doi : 10.1016/j.crma.2005.10.010
Received : 1 June 2005 ;  accepted : 11 October 2005
Schéma volumes finis monotone pour des opérateurs de diffusion fortement anisotropes sur des maillages de triangles non structurés
Finite volume monotone scheme for highly anisotropic diffusion operators on unstructured triangular meshes
 

Christophe Le Potier
Commissariat à lʼénergie atomique, DEN/DM2S/SFME/MTMS, 91191 Gif-sur-Yvette cedex, France 

Résumé

Nous décrivons une nouvelle méthode de volumes finis pour des opérateurs de diffusion fortement anisotropes sur des maillages déformés. Lʼidée du schéma est de calculer les gradients à lʼaide dʼune expression non linéaire. Pour les problèmes instationnaires, si le pas de temps est assez petit, la matrice globale associée à ce schéma est monotone sans condition géométrique sur le maillage et sans condition sur le rapport dʼanisotropie. Nous vérifions numériquement la précision de la méthode par comparaison à une solution analytique. Nous montrons lʼefficacité de lʼalgorithme par comparaison à dʼautres schémas numériques qui ne respectent pas le principe du maximum discret sur le cas étudié. Pour citer cet article : C. Le Potier, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.
Abstract

We introduce a new finite volume method for highly anisotropic diffusion operators on unstructured meshes. The main idea is to calculate the gradient using a nonlinear scheme. For parabolic problems, if the time step is small enough, the resulting global matrix is monotone without geometrical constraints on the mesh and restrictive conditions on the anisotropy ratio. We check the precision of the method in comparison with analytical solutions. The efficiency of the algorithm is demonstrated by comparing it with numerical schemes which do not satisfy a discrete maximum principle on the studied case. To cite this article: C. Le Potier, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.


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