Polyatomic gases with dynamic pressure: Maximum entropy principle and shock structure

TL;DR

This paper develops a maximum entropy-based kinetic model for polyatomic gases with internal energy, analyzing shock structures and comparing with BGK approximation, advancing understanding of non-equilibrium gas dynamics.

Contribution

It introduces a new kinetic model for polyatomic gases using maximum entropy principle and analyzes shock structures, extending previous thermodynamic approaches.

Findings

Constructed a non-equilibrium velocity distribution compatible with macroscopic variables.

Derived collision cross section satisfying micro-reversibility.

Analyzed shock structure within the proposed kinetic framework.

Abstract

This paper is concerned with the analysis of polyatomic gases within the framework of kinetic theory. Internal degrees of freedom are modeled using a single continuous variable corresponding to the molecular internal energy. Non-equilibrium velocity distribution function, compatible with macroscopic field variables, is constructed using the maximum entropy principle. A proper collision cross section is constructed which obeys the micro-reversibility requirement. The source term and entropy production rate are determined in the form which generalizes the results obtained within the framework of extended thermodynamics. They can be adapted to appropriate physical situations due to the presence of parameters. They are also compared with the results obtained using BGK approximation. For the proposed model the shock structure problem is thoroughly analyzed.