A two-temperature six-moment approach to the shock wave problem in a polyatomic gas

Starting from a two-velocity version of a recently derived six-moment closure of the kinetic Boltzmann description of a polyatomic gas, based on a discrete structure of internal energy levels, the classical shock wave problem is analyzed in some detail. Explicit analytical results are achieved under a simplifying assumption equivalent to the standard approximation of polytropic gases, to which this paper is generally restricted. In particular, existence of smooth solutions, occurrence of jumps in the kinetic and excitation temperatures, and possible temperature overshooting are emphasized.