Asymptotic Preserving Spectral Deferred Correction Methods for Hyperbolic Systems with Relaxation

Abstract

In this paper, we consider the semi-implicit spectral deferred correction (SDC) methods for hyperbolic systems of conservation laws with stiff relaxation terms. The relaxation term is treated implicitly, and the convection terms are treated by explicit schemes. The SDC schemes proposed are asymptotic preserving (AP) in the zero relaxation limit and can be constructed easily and systematically for any order of accuracy. Weighted essentially non-oscillatory (WENO) schemes are adopted in spatial discretization to achieve high order accuracy. After a description of the asymptotic preserving property of the SDC schemes, several applications will be presented to demonstrate the stiff accuracy and capability of the schemes.