Numerical Study of Comprehensive Kinetic Model in Plane Shock Wave Problem

The comprehensive kinetic model equation for unsteady one-dimensional flow is numerically solved to obtain a converging solution for a plane shock structure problem. This model equation is proposed by Oguchi on the basis of the Grad’s 13-moment approximation, and its collision term is expressed in an explicit function of the peculiar velocities. The problem is selected as a typical problem for surveying the applicability of the present model to gas dynamic problems. The numerical calculations are performed for Maxwell molecules. The free-stream Mach number range is from 1.05 to 2.0. The resultant shock wave profiles of the number density exhibit reasonable forms with monotonic change, and the resultant shock thickness values agree well with the corresponding Navier-Stokes values. The present results suggest us to open a way for the applicability of the present kinetic model to various gas dynamic problems in weakly rarefied conditions.