Premium
A numerical scheme for a kinetic model for mixtures in the diffusive limit using the moment method
Author(s) -
Bondesan Andrea,
Boudin Laurent,
Grec Bérénice
Publication year - 2019
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22345
Subject(s) - knudsen number , limit (mathematics) , a priori and a posteriori , mach number , diffusion , mathematics , kinetic energy , moment (physics) , scaling , scheme (mathematics) , conservation law , statistical physics , kinetic scheme , conservation of mass , kinetic theory , mathematical analysis , classical mechanics , physics , mechanics , thermodynamics , geometry , philosophy , epistemology
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.