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

Shock structure in extended thermodynamics with second-order maximum entropy principle closure

“…In particular, it was predicted by non-equilibrium models and observed in experiments, that for polyatomic gases like CO 2 , the shock structure profile has a peculiar behavior which substantially differs from the one observed in monatomic gases: the shock structure is characterized in fact, for values of the shock speed smaller than the maximum characteristic speed of the system in the unperturbed equilibrium state, by a very sharp (but continuous) part of the profile, followed by a much less sharp part of the profile. This peculiar feature of the shock profile was obtained both in the framework of extended thermodynamics [31] and in the context of kinetic theory [33,34]. The results presented in [31,33] are replicated in Fig.…”

“…In recent years much research work has been devoted to the analysis of the shock structure in polyatomic gases [5,[31][32][33][34][35]. It is now understood that for several polyatomic gases relevant in practical applications, as for example carbon dioxide (CO 2 ), the dynamic pressure plays a relevant role in nonequilibrium processes, and the model assumption of a single relaxation time for all the involved relaxation processes is not acceptable when the fine structure of processes far from equilibrium is of interest.…”

“…It is found that the solution of the non-linear system ( 35) is qualitatively different from the solution of the system obtained with the first order closure, represented in Eq. (34). A remarkable result is the following.…”

Molecular Extended Thermodynamics of Rarefied Polyatomic Gases with a New Hierarchy of Moments

“…Although there is still no theorem, as we have seen for monatomic gas in [5], it is needed to take many moments to have an optimal agreement with the experiments on such as the high-frequency sound wave, low-angle light scattering, or shock wave with a high Mach number. In the case of polyatomic gases, when the bulk viscosity is very high compared to the shear viscosity, the ET 14 gives excellent results concerning shock waves [44][45][46] and sound waves with high-frequency [47]. However, when the order of the bulk viscosity is the same or smaller the one of the shear viscosity, we have a similar situation to monatomic gases, and we expect the necessity of more moments.…”

BGK and Fokker-Planck Models of the Boltzmann Equation for Gases with Discrete Levels of Vibrational Energy

“…It is therefore interesting to extend the model equations to take this vibrational modes into account. Several extended BGK models have been recently proposed to do so, for instance [16,17,18,19], and a recent Fokker-Planck model has been proposed earlier in [13].…”