arXiv:1204.5092v1 [physics.flu-dyn] 23 Apr 2012 Low Mach number effect in simulation of high Mach number flow X. Y. Hu and N. A. Adams Lehrstuhl f¨ ur Aerodynamik, Technische Universit¨ at M¨ unchen 85748 Garching, Germany Abstract In this note, we relate the two well-known difficulties of Godunov schemes: the carbuncle phenomena in simulating high Mach number flow, and the inaccurate pressure profile in simulating low Mach number flow. We introduced two simple low-Mach-number modifications for the classical Roe flux to decrease the differ- ence between the acoustic and advection contributions of the numerical dissipation. While the first modification increases the local numerical dissipation, the second decreases it. The numerical tests on the double-Mach reflection problem show that both modifications eliminate the kinked Mach stem suffered by the original flux. These results suggest that, other than insufficient numerical dissipation near the shock front, the carbuncle phenomena is strongly relevant to the non-comparable acoustic and advection contributions of the numerical dissipation produced by Go- dunov schemes due to the low Mach number effect. Key words: Low Mach number flow, high Mach number flow, numerical scheme. Preprint submitted to Elsevier March 19, 2018