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.
Mots-clés : porous media, diffusion operator, anisotropy, non conforming meshes
@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 },
pages = {265--290},
publisher = {EDP-Sciences},
volume = {46},
number = {2},
year = {2012},
doi = {10.1051/m2an/2011040},
mrnumber = {2855643},
zbl = {1271.76324},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2011040/}
}
TY - JOUR AU - Eymard, Robert AU - Guichard, Cindy AU - Herbin, Raphaèle TI - Small-stencil 3D schemes for diffusive flows in porous media JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2012 SP - 265 EP - 290 VL - 46 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2011040/ DO - 10.1051/m2an/2011040 LA - en ID - M2AN_2012__46_2_265_0 ER -
%0 Journal Article %A Eymard, Robert %A Guichard, Cindy %A Herbin, Raphaèle %T Small-stencil 3D schemes for diffusive flows in porous media %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2012 %P 265-290 %V 46 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2011040/ %R 10.1051/m2an/2011040 %G en %F 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 , Tome 46 (2012) no. 2, pp. 265-290. doi : 10.1051/m2an/2011040. http://www.numdam.org/articles/10.1051/m2an/2011040/
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