An Asymptotic Preserving Monte Carlo Method for the Multispecies Boltzmann Equation

An asymptotic preserving (AP) scheme is efficient in solving multiscale kinetic equations with a wide range of the Knudsen number. In this paper, we generalize the asymptotic preserving Monte Carlo method (AP-DSMC) developed in [25] to the multispecies Boltzmann equation. This method is based on the successive penalty method [26] originated from the BGK-penalization-based AP scheme developed in [7]. For the multispecies Boltzmann equation, the penalizing Maxwellian should use the unified Maxwellian as suggested in [12]. We give the details of AP-DSMC for multispecies Boltzmann equation, show its AP property, and verify through several numerical examples that the scheme can allow time step much larger than the mean free time, thus making it much more efficient for flows with possibly small Knudsen numbers than the classical DSMC.