A nine-point finite volume scheme for the simulation of diffusion in heterogeneous media |
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| Authors: | Léo Agelas Robert Eymard Raphaèle Herbin |
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| Affiliation: | 1. Institut Français du Pétrole, 1 & 4, avenue de Bois-Préau, 92852 Rueil-Malmaison Cedex, France;2. Laboratoire d''Analyse et de Mathématiques Appliquées, UMR 8050, Université Paris-Est, 5, boulevard Descartes Champs-sur-Marne, F-77454 Marne La Vallée Cedex 2, France;3. Laboratoire d''analyse, topologie et probabilités, Université de Provence, 39, rue Joliot-Curie, 13453 Marseille, France |
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| Abstract: | 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. To cite this article: L. Agelas et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009). |
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