A Kinetic Model for a Polyatomic Gas with Temperature-Dependent Specific Heats and Its Application to Shock-Wave Structure

The ellipsoidal statistical (ES) model of the Boltzmann equation for a polyatomic gas with constant specific heats (calorically perfect gas), proposed by Andries et al. (Eur J Mech B Fluids 19:813, 2000), is extended to a polyatomic gas with temperature-dependent specific heats (thermally perfect gas). Then, the new model equation is applied to investigate the structure of a plane shock wave with special interest in $$\hbox {CO}_2$$ gas, which is known to have a very large bulk viscosity, and in the case of relatively strong shock waves. A numerical analysis, as well as an asymptotic analysis for large bulk viscosity, is performed in parallel to the previous paper by two of the present authors (Kosuge and Aoki, in: Phys Rev Fluids 3:023401, 2018), where the structure of a shock wave in $$\hbox {CO}_2$$ gas was investigated using the ES model for a polyatomic gas with constant specific heats. From the numerical and analytical results, the effect of temperature-dependent specific heats on the structure of a shock wave is clarified.