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Small-stencil 3D schemes for diffusive flows in porous media

Published online by Cambridge University Press:  12 October 2011

Robert Eymard ,
Cindy Guichard  and
Raphaèle Herbin
Robert Eymard
Affiliation:
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,
Cindy Guichard
Affiliation:
IFP Énergies nouvelles, 1 & 4, avenue de Bois-Préau, 92852 Rueil-Malmaison cedex, France. cindy.guichard@ifpen.fr
Raphaèle Herbin
Affiliation:
LATP-CNRS UMR 6632, Aix-Marseille Université, 39 rue Joliot Curie, 13453 Marseille, France. herbin@cmi.univ-mrs.fr,
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Abstract

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.

Keywords

Porous mediadiffusion operatoranisotropynon conforming meshes
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 2 , March 2012 , pp. 265 - 290
Copyright
© EDP Sciences, SMAI, 2011

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