Application of hybrid Riemann solvers based on HLLC and HLL for simulation of flows with gas-dynamic discontinuities

Abstract

Application of hybrid approximate Riemannian 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 it. The second hybrid solver (HLLC-ADC) uses the weighted sum of HLLC and HLL, applying as weights the pressure function at the left and right cell centers. The third hybrid solver (HLLC-HLL) computes inviscid fluxes by HLL inside shock waves, and by HLLC in other areas of the flow. Facets within shock waves are defined by a shock wave indicator based on the reconstructed left and right pressure values of the face. Several tests are performed, and it is shown that hybrid solvers prevent the carbuncle and reduce oscillations on shock waves.