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.

在本文中，提出了在零马赫数限制下对波动方程系统的渐近保持 (AP) IMEX-RK 有限体积方案的分析。采用IMEX-RK方法获得时间半离散格式，并使用标准有限体积技术推导出时空全离散格式。时间半离散和时空全离散方案都建立了唯一数值解的存在性、其相对于马赫数的均匀稳定性以及低马赫数下的精度。该方案的 AP 性质已针对不需要全局严格准确的一般类 IMEX 方案证明。大量的数值案例研究证实了该方案在马赫数和所有上述属性方面的统一二阶收敛。