A review on BGK models for gas mixtures of mono and polyatomic molecules

TL;DR

This review discusses recent BGK models for gas mixtures of monoatomic and polyatomic molecules, focusing on their mathematical properties and how they address multiple species and internal energy modes.

Contribution

It provides a comprehensive overview of recent developments in BGK models for complex gas mixtures and their mathematical analysis.

Findings

Recent BGK models effectively handle multiple species and internal degrees of freedom.

Mathematical theory supports the validity and stability of these models.

Advances facilitate more accurate simulations of real gas behaviors.

Abstract

We consider the socalled Bathnagar-Gross-Krook (BGK) model, an approximation of the Boltzmann equation, describing the time evolution of a single momoatomic rarefied gas and satisfying the same two main properties (conservation properties and entropy inequality). However, in practical applications one often has to deal with two additional physical issues. First, a gas often does not consist of only one species, but it consists of mixture a mixture of different species. Second, the particles can store energy not only in translational degrees of freedom but also in internal degrees of freedom like rotations or vibrations (polyatomic molecules). Therefore, here, we will present recent BGK models for gas mixtures for mono- and polyatomic particles and the existing mathematical theory for these models.