Many low-Mach or all-Mach number codes are based on space discretizations which in combination with the first order explicit Euler method as time integration would lead to an unstable scheme. In this paper, we investigate how the choice of a suitable explicit time integration method can stabilize these schemes. We restrict ourselves to some old prototypical examples in order to find directions for further research in this field.

翻译：许多低马赫数或全马赫数数值计算代码所采用的空间离散格式，若结合一阶显式欧拉方法作为时间积分，将导致格式不稳定。本文通过探究如何选取合适的显式时间积分方法以稳定这类格式，并限于若干经典原型案例，旨在为该领域的后续研究指明方向。