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

The aim of this paper is to construct the molecular extended thermodynamics for classical rarefied polyatomic gases with a new hierarchy, which is absent in the previous procedures of moment equations. The new hierarchy is deduced recently from the classical limit of the relativistic theory of moments associated with the Boltzmann–Chernikov equation. The field equations for 15 moments of the distribution function, in which the internal degrees of freedom of a molecule are taken into account, are closed with the maximum entropy principle. It is shown that the theory contains, as a principal subsystem, the previously polyatomic 14 fields theory, and in the monatomic limit, in which the dynamical pressure vanishes, the differential system converges, instead of to the Grad 13-moment system, to the Kremer 14-moment system.

Refined Navier-Stokes-Fourier Equations for Rarefied Polyatomic Gases

A macroscopic model for the description of rarefied polyatomic gas flows is introduced. Grad’s moment method is used to construct a closed set of equations for 36 primary moments. The order of magnitude method is then applied to acquire optimized moment definitions. The appropriate sets of equations corresponding to the desired order of accuracy in the Knudsen number are derived by reducing the equations. A refined version of the Navier-Stokes-Fourier (NSF) equations is obtained where the dynamic temperature is an additional independent variable.