Study of discrete duality finite volume schemes for the Peaceman model

Claire Chainais-Hillairet 1, 2 Stella Krell 3, 4 Alexandre Mouton 1
2 SIMPAF - SImulations and Modeling for PArticles and Fluids
LPP - Laboratoire Paul Painlevé - UMR 8524, Inria Lille - Nord Europe
4 COFFEE - COmplex Flows For Energy and Environment
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR7351
Abstract : In this paper, we are interested in the finite volume approximation of a system describing miscible displacement in porous media. This system is made of two coupled equations: an anisotropic diffusion equation on the pressure and a convection-diffusion-dispersion equation on the concentration of invading fluid. The anisotropic diffusion operators in both equations require a special care while discretizing by a finite volume method. We focus here on the numerical approximation by some Discrete Duality Finite Volume methods. After the presentation of the scheme, we establish some a priori estimates satisfied by the numerical solution and prove existence and uniqueness of the solution to the scheme. We show the efficiency of the schemes through numerical experiments.
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Claire Chainais-Hillairet, Stella Krell, Alexandre Mouton. Study of discrete duality finite volume schemes for the Peaceman model. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2013, 35 (6), pp.A2928--A2952. ⟨10.1137/130910555⟩. ⟨hal-00790449⟩

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