2020
DOI: 10.48550/arxiv.2007.09951
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Finite volumes for the Stefan-Maxwell cross-diffusion system

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… Show more

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Cited by 2 publications
(8 citation statements)
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References 43 publications
(93 reference statements)
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“…with density h α (c) = n i=1 c i (log(c i ) − µ * ,α i ) − c i + 1, for α ∈ {s, g}, can be shown to satisfy, for some positive semi-definite mobility matrices M s , M g , the free energy dissipation relation [4,5]…”
Section: A Free Interface Cross-diffusion Modelmentioning
confidence: 99%
“…with density h α (c) = n i=1 c i (log(c i ) − µ * ,α i ) − c i + 1, for α ∈ {s, g}, can be shown to satisfy, for some positive semi-definite mobility matrices M s , M g , the free energy dissipation relation [4,5]…”
Section: A Free Interface Cross-diffusion Modelmentioning
confidence: 99%
“…In fact there exists only few papers on this subject. Let us cite [23,25,28,40] where the authors studied, using similar techniques than in this paper, some convergent finite volume schemes for an ion transport, the Maxwell-Stefan, a thin-film solar cells and a biofilm cross-diffusion system with a volume filling constraint. However, in these former works the numerical schemes were designed for particular models.…”
Section: 3mentioning
confidence: 99%
“…) be given for each K ∈ T . Then, the vector (u k , π k ) is solution to the following nonlinear system (25) m(K)…”
Section: Notation and Definitions We Present The Discretization Of Th...mentioning
confidence: 99%
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