An asymptotic preserving numerical scheme for kinetic equations in the low Mach number limit

A numerical scheme for the nonstationary Boltzmann equation in the incompressible Navier-Stokes limit is developed. The scheme is induced by the asymptotic analysis of the Navier-Stokes limit for the Boltzmann equation. It works uniformly for all ranges of mean free paths. In the limit the scheme reduces to the Chorin projection method for the incompressible Navier-Stokes equation. Numerical results for different physical situations are shown and the uniform convergence of the scheme is established numerically.