Kinetic models of BGK type and their numerical integration
It provides a tutorial overview of BGK models and numerical methods for researchers in rarefied gas dynamics, but is largely a review of existing work rather than presenting new results.
This work reviews recent results on BGK-type kinetic models for rarefied gases in weakly non-equilibrium regimes, including polyatomic gases and mixtures, and discusses asymptotic preserving numerical schemes that efficiently approximate equilibrium solutions without resolving fast scales.
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.