Regularized 13-Moment Equations for Inverse Power Law Models

TL;DR

This paper develops a systematic method to derive regularized 13-moment equations for various gas models, demonstrating their stability and effectiveness in capturing shock structures in rarefied gas dynamics.

Contribution

It introduces a general approach to derive stable, regularized moment equations applicable to multiple inverse power law models, including the hard-sphere model.

Findings

Equations are stable near equilibrium.

Models accurately capture shock structures in strong nonequilibrium.

Method is systematic and applicable to various collision models.

Abstract

We propose a systematic methodology to derive the regularized thirteen-moment equations in the rarefied gas dynamics for a general class of linearized collision models. Detailed expressions of the moment equations are written down for all inverse power law models as well as the hard-sphere model. By linear analysis, we show that the equations are stable near the equilibrium. The models are tested for shock structure problems to show its capability to capture the correct flow structure in strong nonequilibirum.