Entropy Stable Numerical Fluxes for Compressible Euler Equations which are Suitable for All Mach Numbers

Abstract: We propose two novel two-state approximate Riemann solvers for the compressible Euler equations which are provably entropy dissipative and suitable for the simulation of low Mach numbers. What is new, is that one of our two methods in addition is provably kinetic energy stable. Both methods are based on the entropy satisfying and kinetic energy consistent methods of Chandrashekar (2013). The low Mach number compliance is achieved by rescaling some speed of sound terms in the diffusion matrix in the spirit of Li & Gu (2008). In numerical tests we demonstrate the low Mach number compliance and the entropy stability of the proposed fluxes.