A numerical scheme for the compressible low-Mach number regime of ideal fluid dynamics
Provides a theoretical foundation and stability analysis for a scheme that addresses the challenge of simulating low-Mach number flows with compressible Euler solvers, benefiting computational fluid dynamics researchers.
The paper analyzes a numerical scheme for compressible low-Mach number flows, showing its limit yields a discretization of the continuous limit system and demonstrating accurate tracking of the Gresho vortex down to Mach numbers of ~1e-10.
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.: New numerical solver for flows at various mach numbers. A&A 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 ~1e-10 .