Comptes Rendus
Algorithm to refine a finite volume mesh admissible for parabolic problems
Comptes Rendus. Mécanique, Volume 337 (2009) no. 2, pp. 95-100.

We present a simple algorithm to refine a finite volume bidimensional mesh admissible to solve elliptic or parabolic partial differential equations. The approximation of the Laplace operator reduces to the one of the normal fluxes along the edges of control volumes. These normal fluxes can be computed in a consistent way by a classical two points flux approximation simple if the mesh is admissible in the finite volume sense. The originality of the mesh refinement technique that we propose, is to preserve the admissibility property of the meshes. Therefore it can be used in a wide classic context.

On présente un algorithme simple de raffinement de maillage bidimensionnel de type volumes finis adapté à la résolution d'équations aux dérivées partielles elliptiques ou paraboliques. L'approximation du Laplacien se ramène à celle de flux normaux sur les arêtes des volumes de contrôle. Le calcul du flux est simple si on choisit les centres des mailles de telle sorte que la droite qui joint deux centres voisins soit toujours orthogonale à leur arête commune (maillage admissible). Le processus de raffinement proposé est original car il permet la construction d'un maillage admissible pouvant être utilisé dans un cadre classique très répandu.

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Accepted:
Published online:
DOI: 10.1016/j.crme.2009.03.001
Keywords: Computational fluid mechanics, Computer science, Finite volume, Mesh refinement, Laplace operator
Mot clés : Mécanique des fluides numériques, Algorithmique, Volumes finis, Raffinement de maillage, Laplacien

Florence Hubert 1; Marie-Claude Viallon 2

1 Université de Provence, CMI, Technopôle de Château Gombert, 39, rue F. Joliot Curie, 13453 Marseille cedex 13, France
2 UFR Sciences de Saint-Etienne, departement de mathématiques, 23, rue du docteur Paul-Michelon, 42023 Saint-Etienne, France
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Florence Hubert; Marie-Claude Viallon. Algorithm to refine a finite volume mesh admissible for parabolic problems. Comptes Rendus. Mécanique, Volume 337 (2009) no. 2, pp. 95-100. doi : 10.1016/j.crme.2009.03.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2009.03.001/

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