A Micro-Macro Decomposition-Based Asymptotic-Preserving Scheme for the Multispecies Boltzmann Equation

Abstract

In this paper we extend the micro-macro decomposition-based asymptotic-preserving scheme developed by Bennoune, Lemou, and Mieussens [J. Comput. Phys., 227 (2008), pp. 3781-3803] for the single species Boltzmann equation to the multispecies problems. An asymptotic-preserving scheme for the kinetic equation is very efficient in the fluid regime where the Knudsen number is small and the collision term becomes stiff. It allows a coarse (independent of the Knudsen number) mesh size and a large time step in the fluid regime. The difficulty associated with multispecies problems is that there are no local conservation laws for each species, resulting in extra stiff nonlinear source terms that need to be discretized properly in order to (1) avoid Newton-type solvers for nonlinear algebraic systems, and (2) to be asymptotic-preserving. We show that these extra nonlinear source terms can be solved using only linear system solvers, and the scheme preserves the correct Euler and Navier-Stokes limits. Numerical examples are used to demonstrate the efficiency and applicability of the schemes for both Euler and Navier-Stokes regimes.