An Evaluation of Euler Fluxes for Hypersonic Flow Computations
摘要：
Shock-capturing finite volume schemes often give rise to anomalous results in hypersonic flow. We present a wide-ranging survey of numerical experiments from 12 different flux functions in one- and two-dimensional contexts. Included is a recently developed function that satisfies the second law of thermodynamics. It is found here that there are at least two kinds of shock instabilities: one is one-dimensional and the other is multidimensional. According to the results, the former does not appear if a flux function satisfies the second law of thermodynamics, and the latter is suppressed by an additional dissipation with a multidimensional character. However, such dissipation has no effect on the one-dimensional mode. Among the flux functions investigated, no universally stable schemes are found that are free from both one- and multidimensional shock instabilities. The appearance of these instabilities depends-on the relative positioning of the shock on the grid.
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关键词：
e: internal energy, (p/ρ)/(γ-1) e_t: total energy, e + (1/2)(u~2 + v~2) H: total enthalpy, e_t + p/ρ i, j: cell indices M: Mach number et al
DOI：
10.2514/1.33735
被引量：
年份：
2007
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