A SUCCESSIVE PENALTY-BASED ASYMPTOTIC-PRESERVING SCHEME FOR KINETIC EQUATIONS

作者：Yan, Bokai^*; Jin, Shi

来源：SIAM Journal on Scientific Computing, 2013, 35(1): A150-A172.

DOI：10.1137/110857982

• asymptotic-preserving schemes
• kinetic equations
• successive penalization

We propose an asymptotic-preserving (AP) scheme for kinetic equations that is efficient also in the hydrodynamic regimes. This scheme is based on the Bhantnagar-Gross-Krook (BGK) penalty method introduced by Filbet and Jin [J. Comput. Phys., 229 (2010), pp. 7625-7648], but uses the penalization successively to achieve the desired asymptotic property. This method possesses a stronger AP property than the original method of Filbet and Jin, with the additional feature of being positivity preserving when applied on the Boltzmann equation. It is also general enough to be applicable to several important classes of kinetic equations, including the Boltzmann equation and the Landau equation. Numerical experiments verify these properties.

• 出版日期2013
• 单位上海交通大学