Relaxation scheme for a lattice-Boltzmann-type discrete velocity model and numerical Navier-Stokes limit

A discrete velocity model based on a lattice-Boltzmann approximation is considered in the low Mach number limit. A numerical scheme for this model working uniformly in the incompressible Navier-Stokes limit is constructed. The scheme is induced by the asymptotic analysis of the Navier-Stokes Limit and works uniformly for all ranges of mean free paths. In the limit the scheme reduces to an explicit finite difference scheme for the incompressible Navier-Stokes equation, the Chorin projection method with MAC grid. Numerical results are presented and the uniform convergence of the scheme is established numerically. (C) 1999 Academic Press.