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In this paper the analysis of an asymptotic preserving (AP) IMEX-RK finitevolume scheme for the wave equation system in the zero Mach number limit ispresented. The accuracy of a numerical scheme at low Mach numbers is itsability to maintain the solution close to the incompressible solution for alltimes, and this can be formulated in terms of the invariance of a space ofconstant densities and divergence-free velocities. An IMEX-RK methodology isemployed to obtain a time semi-discrete scheme, and a space-time fully-discretescheme is derived by using standard finite volume techniques. The existence ofa unique numerical solution, its uniform stability with respect to the Machnumber, the AP property, and the accuracy at low Mach numbers are establishedfor both time semi-discrete, and space-time fully-discrete schemes. Extensivenumerical case studies confirm uniform second order convergence of the schemewith respect to the Mach number, and all the above-mentioned properties.

Analysis of an Asymptotic Preserving Low Mach Number Accurate IMEX-RK Scheme for the Wave Equation System