Analysis of an asymptotic preserving low mach number accurate IMEX-RK scheme for the wave equation system

Abstract

In this paper the analysis of an asymptotic preserving (AP) IMEX-RK finite volume scheme for the wave equation system in the zero Mach number limit is presented. An IMEX-RK methodology is employed to obtain a time semi-discrete scheme, and a space-time fully-discrete scheme is derived by using standard finite volume techniques. The existence of a unique numerical solution, its uniform stability with respect to the Mach number, and the accuracy at low Mach numbers are established for both time semi-discrete and space-time fully-discrete schemes. The AP property of the scheme is proved for a general class of IMEX schemes which need not be globally stiffly accurate. Extensive numerical case studies confirm uniform second order convergence of the scheme with respect to the Mach number and all the above-mentioned properties.