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.
@article{M2AN_2012__46_2_265_0,
author = {Eymard, Robert and Guichard, Cindy and Herbin, Rapha\`ele},
title = {Small-stencil 3D schemes for diffusive flows in porous media},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {46},
year = {2012},
pages = {265-290},
doi = {10.1051/m2an/2011040},
mrnumber = {2855643},
zbl = {1271.76324},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2012__46_2_265_0}
}
Eymard, Robert; Guichard, Cindy; Herbin, Raphaèle. Small-stencil 3D schemes for diffusive flows in porous media. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 46 (2012) pp. 265-290. doi : 10.1051/m2an/2011040. http://gdmltest.u-ga.fr/item/M2AN_2012__46_2_265_0/
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