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Article Dans Une Revue SIAM Journal on Scientific Computing Année : 2013

Study of discrete duality finite volume schemes for the Peaceman model

Résumé

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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hal-00790449 , version 1 (20-02-2013)

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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, 2013, 35 (6), pp.A2928--A2952. ⟨10.1137/130910555⟩. ⟨hal-00790449⟩
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