Evaluation of Euler Fluxes for Hypersonic Flow Computations

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 t...

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Bibliographic Details
Published in:AIAA journal 2009-01, Vol.47 (1), p.44-53
Main Authors: Kitamura, Keiichi, Roe, Philip, Ismail, Farzad
Format: Article
Language:English
Subjects:
Aerodynamics
Compressible flows
shock and detonation phenomena
Computational methods in fluid dynamics
Eulers equations
Exact sciences and technology
Experiments
Flow control
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Physics
Shock-wave interactions and shock effects
Thermodynamics
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Summary: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. [PUBLICATION ABSTRACT]
ISSN:0001-1452
1533-385X
DOI:10.2514/1.33735