A review on a general multi-species BGK model: modelling, theory and numerics

TL;DR

This review paper discusses a general multi-species BGK kinetic model for gas mixtures, covering its formulation, theoretical properties, and numerical methods, highlighting its flexibility and efficiency in simulating gas dynamics.

Contribution

It provides a comprehensive overview of a flexible multi-species BGK model, including its formulation, theoretical analysis, and numerical approaches, unifying various special cases in the literature.

Findings

The model encompasses various existing BGK models as special cases.

Theoretical results on existence and stability are summarized.

Numerical schemes for the model are reviewed and analyzed.

Abstract

In this article we focus on kinetic equations for gas mixtures since in applications one often has to deal with mixtures instead of a single gas. In particular we consider an approximation of the Boltzmann equation, the Bathnagar-Gross-Krook (BGK) equation. This equation is used in many applications because it is very efficient in numerical simulations. In this article, we recall a general BGK equation for gas mixtures which has free parameters. Specific choices of these free parameters lead to special cases in the literature. For this model, we provide an overview concerning modelling, theoretical results and numerics.