A Successive Penalty-based Asymptotic-Preserving Scheme For Hyperbolic Systems With Stiff Relaxation

We consider a successive penalty-based Asymptotic-Preserving (AP) scheme forhyperbolic systems with stiff relaxation in this paper,such systems arise in reactinggases,shallow water equations,discrete-velocity kinetic models,etc[3].Successive penalty-based AP scheme is based on the AP scheme introduced byFrancis Filbet and Shi Jin(2010)[1],then according to the successive penalty-basedAP scheme for the Boltzmann equation and Landau equation introduced by BokaiYan and Shi Jin(2011)[2],we uses the penalization successively to achieve the desiredasymptotic property for nonlinear hyperbolic equations with stiff relaxation–succes-sive penalty-based AP scheme.This method possesses a stronger AP property than theoriginal method of Filbet-Jin,and also it is general enough to be applicable.Numericalexperiments verify these properties.