An accurate and robust HLLC‐type Riemann solver for the compressible Euler system at various Mach numbers

Abstract

SummaryA simple, robust, and accurate HLLC‐type Riemann solver for the compressible Euler equations at various Mach numbers is built. To cure shock instability of the HLLC solver at strong shocks, a pressure‐control technique, which plays a role in limiting the propagation of erroneous pressure perturbation, is proposed. With an all Mach correction method for the compressible Euler system, the proposed method is further extended to compute flow problems at low Mach numbers. The proposed all Mach HLLC‐type scheme has been implemented and used to compute a variety of flow problems ranging from hypersonic compressible to low Mach incompressible flow regimes. Various numerical results demonstrate that the obtained all Mach HLLC‐type scheme is both accurate and stable for all speed ranges.