On the Carbuncle Origins from Moving and Stationary Shocks
Hypersonic flow computations still suffer from anomalous solutions such as a “carbuncle phenomenon” [1-3]. We still lack an accepted explanation for those anomalies, and we feel there is no single cause, nor is there any single cure. In the present study, we take the viewpoint that the shock anomalies are partly caused by the lack of mathematical expression for internal shock structure by the governing equations, and that they can be examined by numerical experiments. Quirk  introduced a benchmark test for numerical schemes on their responses to the captured (fast) moving shock. In this test, the shock took all the possible locations within a cell but instantly passed through them. Roberts  chose a more slowly moving shock which took 50 time steps to travel a single cell, and discussed a post-shock numerical noise propagation. Kitamura et al.  dealt with a stationary shock located within a cell with an initial shock position parameter ε=0.0, 0.1, ..., 0.9, i.e., the shock was placed at one of 10 possible locations in a cell. Their study discovered that any flux functions including FVS by Van Leer  are prone to carbuncles, though some of those methods had been believed to be carbuncle-free accoring to Quirk . In other words, Quirk’s test for a moving shock was not enough to examine robustness of a numerical flux for a stationary shock. Moreover, in spite of those findings, the origin of the carbuncle remained a mystery. The present study will pursue its clue by bridging the gap between the works explained above, i.e., by varying the shock propagation speed from 0 of Kitamura et al. to 6 in Quirk’s choice and beyond. Following our earlier work, different flux functions by Roe , Van Leer , Liou (AUSM + − up ), and Shima and Kitamura (SLAU ) will be used since they have different degrees of robustness against the shock.
KeywordsStationary Shock Hypersonic Flow Shock Strength Flux Function Single Cure
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