On Godunov-type methods near low densities
Journal of Computational Physics
On WAF-type schemes for multidimensional hyperbolic conservation laws
Journal of Computational Physics
On the Choice of Wavespeeds for the HLLC Riemann Solver
SIAM Journal on Scientific Computing
Mass flux schemes and connection to shock instability
Journal of Computational Physics
Numerical Instablilities in Upwind Methods: Analysis and Cures for the “Carbuncle” Phenomenon
Journal of Computational Physics
Cures for the shock instability: development of a shock-stable Roe scheme
Journal of Computational Physics
Hi-index | 31.45 |
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 Harten-Lax-van Leer contact (HLLC) scheme. By defining a sensing function in the transverse direction of strong shock, the HLLC flux is switched to the Harten-Lax-van 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 HLLC-HLL. It is tested against a steady normal shock instability problem and Quirk's test problems, and spurious solutions in the strong shock regions are successfully controlled.