Navier-Stokes Equations and Bulk Viscosity for a Polyatomic Gas with Temperature-Dependent Specific Heats

A system of Navier-Stokes-type equations with two temperatures is derived, for a polyatomic gas with temperature-dependent specific heats (thermally perfect gas), from the ellipsoidal statistical (ES) model of the Boltzmann equation extended to such a gas. Subsequently, the system is applied to the problem of shock-wave structure for a gas with large bulk viscosity (or, equivalently, with slow relaxation of the internal modes), and the numerical results are compared with those based on the ordinary Navier-Stokes equations. It is shown that the latter equations fail to describe the double-layer structure of shock profiles for a gas with large bulk viscosity.