We present a quantitative comparison between two different Implicit-Explicit Runge-Kutta (IMEX-RK) approaches for the Euler equations of gas dynamics, specifically tailored for the low Mach limit. In this regime, a classical IMEX-RK approach involves an implicit coupling between the momentum and energy balance so as to avoid the acoustic CFL restriction, while the density can be treated in a fully explicit fashion. This approach leads to a mildly nonlinear equation for the pressure, which can be solved according to a fixed point procedure. An alternative strategy consists of employing a semi-implicit temporal integrator based on IMEX-RK methods (SI-IMEX-RK). The stiff dependence is carefully analyzed, so as to avoid the solution of a nonlinear equation for the pressure also for equations of state (EOS) of non-ideal gases. The spatial discretization is based on a Discontinuous Galerkin (DG) method, which naturally allows high-order accuracy. The asymptotic-preserving (AP) and the asymptotically-accurate (AA) properties of the two approaches are assessed on a number of classical benchmarks for ideal gases and on their extension to non-ideal gases.

翻译：本文针对低马赫数极限情形，对气体动力学欧拉方程的两种隐式-显式龙格-库塔（IMEX-RK）方法进行定量比较。在此区域中，经典IMEX-RK方法通过动量与能量平衡的隐式耦合来规避声学CFL限制，而密度可采用全显式处理。该方法会导出关于压力的弱非线性方程，可通过不动点迭代求解。另一种策略是采用基于IMEX-RK方法的半隐式时间积分器（SI-IMEX-RK）。通过精细分析刚性依赖关系，该方法即使对于非理想气体的状态方程（EOS）也能避免求解压力非线性方程。空间离散采用间断伽辽金（DG）方法，该方法天然具备高阶精度。通过在理想气体的经典基准测试及其向非理想气体的扩展案例中，系统评估了两种方法的渐近保持（AP）与渐近精确（AA）特性。