Accuracy and Stability Analysis of the Semi-Lagrangian Method for Stiff Hyperbolic Relaxation Systems and Kinetic BGK Model

In this paper, we develop a family of third order asymptotic-preserving (AP) and asymptotically accurate (AA) diagonally implicit Runge–Kutta (DIRK) time discretization methods for the stiff hyperbolic relaxation systems kinetic Bhatnagar–Gross–Krook (BGK) model in semi-Lagrangian (SL) setting. The are constructed based on an accuracy analysis SL scheme BGK limiting fluid regime when Knudsen number approaches 0. An extra condition asymptotic is derived. Linear von Neumann stability proposed DIRK performed to simplified two-velocity linear model. Extensive numerical tests presented demonstrate AA, AP, properties our schemes.