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Kinetic models of BGK type and their numerical integration. (English) Zbl 1433.82006
Summary: 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.
MSC:
82B40 Kinetic theory of gases in equilibrium statistical mechanics
35B40 Asymptotic behavior of solutions to PDEs
35Q20 Boltzmann equations
82M99 Basic methods in statistical mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82-10 Mathematical modeling or simulation for problems pertaining to statistical mechanics
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