Kinetic models of BGK type and their numerical integration

TL;DR

This paper reviews recent modeling approaches for rarefied gases using BGK-type kinetic models and discusses numerical schemes, especially asymptotic preserving methods, for efficient and accurate simulation of these equations.

Contribution

It provides a comprehensive overview of BGK models for polyatomic gases and mixtures, and discusses numerical integration techniques addressing computational challenges.

Findings

Development of asymptotic preserving schemes for BGK models

Extension of models to polyatomic gases and mixtures

Improved numerical methods for kinetic equations

Abstract

This minicourse contains a description of recent results on the modelling of rarefied gases in weakly non equilibrium regimes, and the numerical methods used to approximate the resulting equations. Therefore this work focuses on BGK type approximations, rather than on full Boltzmann models. Within this framework, models for polyatomic gases and for mixtures will be considered. We will also address numerical issues characteristic of the difficulties one encounters when integrating kinetic equations. In particular, we will consider asymptotic preserving schemes, which are designed to approximate equilibrium solutions, without resolving the fast scales of the approach to equilibrium.