A linear and accurate diffusion scheme respecting the maximum principle on distorted meshes

Vincent Siess

doi:10.1016/j.crma.2009.10.004

Numerical Analysis

A linear and accurate diffusion scheme respecting the maximum principle on distorted meshes

Presented by: Olivier Pironneau

Vincent Siess ¹

¹Commissariat à l'energie atomique, 91680 Bruyères-le-Châtel, France

Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1317-1320

Abstract (Original language)
Résumé

This Note is devoted to the presentation of a linear diffusion scheme that respects the maximum principle on very distorted meshes. The main idea is to use a classical Finite Volumes scheme and to perform a first integration on the Voronoï mesh based on the centers of the cells. A second integration on the primary mesh is then performed. By construction the scheme preserves the maximum principle. A numerical example is also given.

Cette Note est consacrée à la présentation d'un schéma de diffusion qui respecte le principe du maximum sur des maillages très déformés. L'idée essentielle consiste à utiliser un schéma de Volumes Finis classique sur le maillage de Voronoï basé sur les barycentres des mailles primales. On procède alors à une deuxième intégration sur les mailles primales. Par construction, le schéma respecte le principe du maximum. Un exemple numérique est fourni.

Received: 2009-06-18
Accepted: 2009-09-28
Published online: 2009-10-21

DOI: 10.1016/j.crma.2009.10.004

Author's affiliations:

Vincent Siess ¹

¹ Commissariat à l'energie atomique, 91680 Bruyères-le-Châtel, France

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Vincent Siess. A linear and accurate diffusion scheme respecting the maximum principle on distorted meshes. Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1317-1320. doi: 10.1016/j.crma.2009.10.004

References
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