New options for explicit all Mach number schemes by suitable choice of time integration methods

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.