A Moment Solution of Comprehensive Kinetic Model Equation for Shock Wave Structure

Abstract

We consider the classic problem of a one‐dimensional steady shock‐wave solution of the Boltzmann kinetic equation utilizing a new type of 13‐moment approximation proposed by Oguchi (1998). The model, unlike previous ones, expresses the collision term in an explicit function of the molecular velocity. We can thus obtain moment integrals directly because of its explicit expression. The principal value is utilized for the moment integral to cope with the singularity, and we can have five relations for five unknown functions to be determined as functions of the coordinate x. These can be reduced to a first‐order differential equation that can be solved to provide the familiar smooth monotonic transition from the upstream supersonic state to the subsonic downstream state. Computed values of shock thickness for various shock Mach numbers compare well with some existing results obtained by different models and methods to certain Mach numbers beyond which no solution exists. Some problems concerning the existence of solution are considered in Appendix.