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Robust HLLC Riemann solver with weighted average flux scheme for strong shock. (English) Zbl 1391.76556
Summary: 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.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76L05 Shock waves and blast waves in fluid mechanics
Software:
HLLE
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