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Convergence analysis of a DDFV scheme for a system describing miscible fluid flows in porous media

Claire Chainais-Hillairet 1, 2 Stella Krell 3, 4 Alexandre Mouton 2
1 MEPHYSTO - Quantitative methods for stochastic models in physics
LPP - Laboratoire Paul Painlevé - UMR 8524, Inria Lille - Nord Europe, ULB - Université libre de Bruxelles
4 COFFEE - COmplex Flows For Energy and Environment
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR7351
Abstract : In this paper, we prove the convergence of a discrete duality finite volume scheme for a system of partial differential equations 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. We first establish some a priori estimates satisfied by the sequences of approximate solutions. Then, it yields the compactness of these sequences. Passing to the limit in the numerical scheme, we finally obtain that the limit of the sequence of approximate solutions is a weak solution to the problem under study.
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Submitted on : Thursday, January 16, 2014 - 4:28:48 PM
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Claire Chainais-Hillairet, Stella Krell, Alexandre Mouton. Convergence analysis of a DDFV scheme for a system describing miscible fluid flows in porous media. Numerical Methods for Partial Differential Equations, Wiley, 2014, pp.38. ⟨10.1002/num.21913⟩. ⟨hal-00929823⟩

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