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Finite Volumes for the Stefan-Maxwell Cross-Diffusion System

Clément Cancès 1 Virginie Ehrlacher 2, 3 Laurent Monasse 4
1 RAPSODI - Reliable numerical approximations of dissipative systems
LPP - Laboratoire Paul Painlevé - UMR 8524, Inria Lille - Nord Europe
3 MATHERIALS - MATHematics for MatERIALS
CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique, Inria de Paris
4 COFFEE - COmplex Flows For Energy and Environment
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR7351
Abstract : The aim of this work is to propose a provably convergent finite volume scheme for the so-called Stefan-Maxwell model, which describes the evolution of the composition of a multi-component mixture and reads as a cross-diffusion system. The scheme proposed here relies on a two-point flux approximation, and preserves at the discrete level some fundamental theoretical properties of the continuous models, namely the non-negativity of the solutions, the conservation of mass and the preservation of the volume-filling constraints. In addition, the scheme satisfies a discrete entropy-entropy dissi-pation relation, very close to the relation which holds at the continuous level. In this article, we present this scheme together with its numerical analysis, and finally illustrate its behaviour with some numerical results.
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Submitted on : Monday, July 20, 2020 - 11:08:23 AM
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Clément Cancès, Virginie Ehrlacher, Laurent Monasse. Finite Volumes for the Stefan-Maxwell Cross-Diffusion System. 2020. ⟨hal-02902672⟩

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