Kinetic Equations for Polyatomic Gases: The 17-Moment Approximation

Abstract

A set of kinetic equations for polyatomic gases is obained by extending the 13-moment approximation of Grad to solve the inelastic Boltzmann equation of Wang Chang, Uhlenbeck, and de Boer. It is expected that the resulting 17-moment approximation (the four additional moments are the internal temperature and the internal heat flux vector) will be applicable to a wider class of physical problems than the “normal”-type Chapman-Enskog solutions to the inelastic Boltzmann equation. In particular, the kinetic equations should prove quite useful in the study of shock structure and sound propagation in polyatomic gases. As examples, the 17-moment approximation is applied to near equilibrium and relaxation type flows; and all the essential features of the Wang Chang et al. analysis are recovered, such as those involving temperature equilibration, volume viscosity, and the extension of the Navier-Stokes equations to polyatomic gases. In addition, corrections to the Navier-Stokes equations are derived involving terms which are second order in the transport coefficients. Possible generalizations and extensions of the 17-moment approximation are also discussed.