{We analyze a general Implicit-Explicit (IMEX) time discretization for the compressible Euler equations of gas dynamics, showing that they are asymptotic-preserving (AP) in the low Mach number limit. The analysis is carried out for a general equation of state (EOS). We consider both a single asymptotic length scale and two length scales. We then show that, when coupling these time discretizations with a Discontinuous Galerkin (DG) space discretization with appropriate fluxes, an all Mach number numerical method is obtained. A number of relevant benchmarks for ideal gases and their non-trivial extension to non-ideal EOS validate the performed analysis.

翻译：我们分析了气体动力学可压缩欧拉方程的一种通用显式-隐式（IMEX）时间离散格式，证明了该类格式在马赫数趋近零极限下具有渐进保持（AP）特性。该分析针对一般状态方程（EOS）展开，同时考虑了单一渐近长度尺度和双重长度尺度两种情形。进一步研究表明，当将该时间离散格式与采用适当通量的间断伽辽金（DG）空间离散格式耦合时，可得到适用于全马赫数的数值方法。一系列针对理想气体及其向非理想状态方程非平凡推广的相关基准测试验证了上述分析的有效性。