Small-stencil 3D schemes for diffusive flows in porous media
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 2, pp. 265-290.

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.

DOI : 10.1051/m2an/2011040
Classification : 65N30, 65N08, 76S05
Mots clés : porous media, diffusion operator, anisotropy, non conforming meshes
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     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},
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     year = {2012},
     doi = {10.1051/m2an/2011040},
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     zbl = {1271.76324},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/m2an/2011040/}
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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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