Robust HLLC Riemann solver with weighted average flux scheme for strong shock

Sung Don Kim, Bok Jik Lee, Hyoung Jin Lee, In Seuck Jeung*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

81 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)7634-7642
Number of pages9
JournalJournal of Computational Physics
Issue number20
StatePublished - Nov 1 2009
Externally publishedYes


  • HLL scheme
  • HLLC scheme
  • Shock instability
  • Switching function
  • WAF scheme

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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