Robust HLLC Riemann solver with weighted average flux scheme for strong shock
Many researchers have reported failures of the approximate Riemann solvers in the presence of strong shock. This is believed to be due to perturbation transfer in the transverse direction of shock waves. We propose a simple and clear method to prevent such problems for the HartenLaxvan Leer contact (HLLC) scheme. By defining a sensing function in the transverse direction of strong shock, the HLLC flux is switched to the HartenLaxvan Leer (HLL) flux in that direction locally, and the magnitude of the additional dissipation is automatically determined using the HLL scheme. We combine the HLLC and HLL schemes in a single framework using a switching function. High-order accuracy is achieved using a weighted average flux (WAF) scheme, and a method for v-shear treatment is presented. The modified HLLC scheme is named HLLCHLL. It is tested against a steady normal shock instability problem and Quirks test problems, and spurious solutions in the strong shock regions are successfully controlled.
hll scheme switching function hllc scheme hllchll shock instability waf scheme