A Successive Penalty-Based Asymptotic-Preserving Scheme for Kinetic Equations

We propose an asymptotic-preserving (AP) scheme for kinetic equations that is efficient also in the hydrodynamic regimes. This scheme is based on the BGK-penalty method introduced by Filbet-Jin [14], but uses the penalization successively to achieve the desired asymptotic property. This method possesses a stronger AP property than the original method of Filbet-Jin, with the additional feature of being also 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.