Application of Hybrid Riemann Solvers Based on HLLC and HLL for Simulation of Flows with Gas-Dynamic Discontinuities

Abstract

The application of hybrid approximate Riemann solvers based on standard HLLC and HLL solvers is discussed. Three different hybrid solvers are considered. The first hybrid solver (rHLLC-HLL) uses a weighted sum of HLLC and HLL so that HLLC is applied in the direction normal to the shock wave, while HLL is applied in the direction along the wave. The second hybrid solver (HLLC-ADC) uses the weighted sum of HLLC and HLL, applying as weights the pressure function at the centers of the left and right cells. The third hybrid solver (HLLC-HLL) computes inviscid fluxes using HLL inside shock waves and HLLC in the other areas of the flow. The faces within the shock waves are determined by a shock-wave indicator based on the reconstructed pressure values to the left and to the right of the face. Several tests have been carried out showing that hybrid solvers prevent the emergence of carbuncle and reduce oscillations on shock waves.