A Numerical Scheme for the Compressible Low-Mach Number Regime of Ideal Fluid Dynamics

Based on the Roe solver a new technique that allows to correctly represent low Mach number flows with a discretization of the compressible Euler equations was proposed in Miczek et al. (Astron Astrophys 576:A50, 2015). We analyze properties of this scheme and demonstrate that its limit yields a discretization of the continuous limit system. Furthermore we perform a linear stability analysis for the case of explicit time integration and study the performance of the scheme under implicit time integration via the evolution of its condition number. A numerical implementation demonstrates the capabilities of the scheme on the example of the Gresho vortex which can be accurately followed down to Mach numbers of .