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

TL;DR

This paper develops a new hierarchy of moments for polyatomic gases in extended thermodynamics, using the maximum entropy principle, unifying and extending previous models with a consistent classical limit.

Contribution

It introduces a novel hierarchy of moments for polyatomic gases and derives a closed system using maximum entropy, connecting to existing theories in the classical limit.

Findings

The new hierarchy generalizes previous models for polyatomic gases.

The system reduces to known models in specific limits, such as Grad's 13-moments.

The theory ensures a consistent classical limit for different gas types.

Abstract

Recently, Pennisi and Ruggeri [J Stat Phys 179, 231-246 (2020)] consider the classical limit of the relativistic theory of moments associated with the Boltzmann-Chernikov equation truncated at a tensorial index $N+1$ and they proved that there exists a unique possible choice of the moments in the classical case for a given $N$ both for monatomic and polyatomic gases. In particular, in polyatomic gases, there exists a new hierarchy of moments that is more general than the one considered in the recent literature. As consequence, when $N=2$, in the classical limit, there is a theory with $15$ fields. In this paper, we consider this system of moments, and we close the system using 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 to Grad 13-moments system to the 14 moments theory proposed by Kremer [Annales de l'I.H.P. Physique th\'eorique, 45, 419-440 (1986)].