Numerical Passage from Kinetic to Fluid Equations

A numerical way to pass from the Bhatnagar–Gross–Krook model of the Boltzmann equation to compressible Euler equations is presented. In order to do so, a stable discretization of the kinetic equation, valid for arbitrary values of the mean free path is described. This requires that the discretization preserves some physical properties: positivity, conservation of mass, momentum, energy, and entropy property. This is motivated by hypersonic computations for reentry problems.