Convergence analysis of a DDFV scheme for a system describing miscible fluid flows in porous mediaReport as inadecuate




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1 MEPHYSTO - Quantitative methods for stochastic models in physics LPP - Laboratoire Paul Painlevé, ULB - Université Libre de Bruxelles Bruxelles, Inria Lille - Nord Europe 2 LPP - Laboratoire Paul Painlevé 3 JAD - Laboratoire Jean Alexandre Dieudonné 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.

Keywords : porous medium miscible fluid flows finite volume method convergence analysis





Author: Claire Chainais-Hillairet - Stella Krell - Alexandre Mouton -

Source: https://hal.archives-ouvertes.fr/



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