| Issue |
ESAIM: M2AN
Volume 46, Number 2, November-December 2012
|
|
|---|---|---|
| Page(s) | 265 - 290 | |
| DOI | https://doi.org/10.1051/m2an/2011040 | |
| Published online | 12 October 2011 | |
Small-stencil 3D schemes for diffusive flows in porous media
1
LAMA-CNRS UMR 8050, Université Paris-Est Marne-la-Vallée, 5 boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée cedex 2, France. robert.eymard@univ-mlv.fr,
2
IFP Énergies nouvelles, 1 & 4, avenue de Bois-Préau, 92852 Rueil-Malmaison cedex, France. cindy.guichard@ifpen.fr
3
LATP-CNRS UMR 6632, Aix-Marseille Université, 39 rue Joliot Curie, 13453 Marseille, France. herbin@cmi.univ-mrs.fr,
Received:
28
November
2010
Revised:
25
April
2011
In this paper, we study some discretization schemes for diffusive flows in heterogeneous anisotropic porous media. We first introduce the notion of gradient scheme, and show that several existing schemes fall into this framework. Then, we construct two new gradient schemes which have the advantage of a small stencil. Numerical results obtained for real reservoir meshes show the efficiency of the new schemes, compared to existing ones.
Mathematics Subject Classification: 65N30 / 65N08 / 76S05
Key words: Porous media / diffusion operator / anisotropy / non conforming meshes
© EDP Sciences, SMAI, 2011
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