A numerical scheme for a kinetic model for mixtures in the diffusive limit using the moment method

Abstract : In this article, we consider a multi-species kinetic model which leads to the Maxwell-Stefan equations under a standard diffusive scaling (small Knudsen and Mach numbers). We propose a suitable numerical scheme which approximates both the solution of the kinetic model in rarefied regime and the one in the diffusion limit. We prove some a priori estimates (mass conservation and nonnegativity) and well-posedness of the discrete problem. We also present numerical examples where we observe the asymptotic-preserving behavior of the scheme.
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Andrea Bondesan, Laurent Boudin, Bérénice Grec. A numerical scheme for a kinetic model for mixtures in the diffusive limit using the moment method. Numerical Methods for Partial Differential Equations, Wiley, In press, 35 (3), pp.1184-1205. ⟨10.1002/num.22345⟩. ⟨hal-01727725⟩

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