Macroscopic equations for rarefied gas dynamics

Abstract

We propose a modification of the procedure for deriving continuum equations from kinetic theory. Though we start in the customary way from an expansion in mean free path, we do not apply solvability conditions in each order, as is usually done. Thus we obtain a partial sum of the series in mean free path that is a more general approximation to a solution of the kinetic equation than in the standard approaches. We illustrate results from this method with expressions for the pressure tensor and heat flux vector derived from the relaxation (or BGK) model of kinetic theory. These expressions generalize those of the Navier–Stokes equations, to which they reduce for small mean free path. When we compute thicknesses of shock waves and phase speeds of ultrasonic waves from the theory, we obtain results that are in good agreement with experimental data, even for long mean free paths of particles.