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

In this paper, we study some discretization schemes for diffusing flows in heterogeneous anisotropic porous media. We first introduce the notion of gradient scheme, and show that several existing schemes fall in 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.

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