A relaxation system based on a Lattice-Boltzmann type discrete velocity model is considered in the low Mach number limit. A third order relaxation scheme is developed working uniformly for all ranges of the mean free path and Mach number. In the incompressible Navier-Stokes limit the scheme reduces to an explicit high order finite difference scheme for the incompressible Navier-Stokes equations based on nonoscillatory upwind discretization. Numerical results and comparisons with other approaches are presented for several test cases in one and two space dimensions.
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