Asymptotic-Preserving Schemes for the Initial-Boundary Value Problem of Hyperbolic Relaxation Systems

SIAM Journal on Scientific Computing, vol. 48, pp. A2833–A2856

Abstract

Abstract. In this work, we present a numerical method for the initial-boundary value problem (IBVP) of first-order hyperbolic systems with source terms. The scheme directly solves the relaxation system using a relatively coarse mesh and captures the equilibrium behavior quite well, even in the presence of boundary layers. This method extends the concept of asymptotic-preserving schemes from initial-value problems (IVPs) to IBVPs. Moreover, we apply this idea to design a unified numerical scheme for the interface problem of relaxation systems.

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