Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 228, Issue 20, Pages 7634-7642Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2009.07.006
Keywords
HLLC scheme; HLL scheme; WAF scheme; Shock instability; Switching function; HLLC-HLL
Funding
- Brain Korea 21 Project in SNU
- Korea government (MEST) [R01-2008-000-12362-0]
- National Research Foundation of Korea [R01-2008-000-12362-0, 과C6A1803, 2008-0060279] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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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. (C) 2009 Elsevier Inc. All rights reserved.
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