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.