An Accurate and Robust Flux Splitting Scheme for Shock and Contact Discontinuities

A flux splitting scheme (AUSMDV) has been constructed with an aim at removing numerical dissipation of the Van Leer-type flux vector splittings on a contact discontinuity. The obtained scheme is also recognized as an improved advection upstream splitting method (AUSM) by Liou and Steffen. The propos...

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Bibliographic Details
Published in:SIAM journal on scientific computing 1997-05, Vol.18 (3), p.633-657
Main Authors: Wada, Yasuhiro, Liou, Meng-Sing
Format: Article
Language:English
Subjects:
Coordinate transformations
Entropy
Navier-Stokes equations
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Summary:A flux splitting scheme (AUSMDV) has been constructed with an aim at removing numerical dissipation of the Van Leer-type flux vector splittings on a contact discontinuity. The obtained scheme is also recognized as an improved advection upstream splitting method (AUSM) by Liou and Steffen. The proposed scheme has the following favorable properties: accurate and robust resolution for shock and contact (steady and moving) discontinuities; conservation of enthalpy for steady flows; algorithmic simplicity; and easy extension to general conservation laws such as that for chemically reacting flows. A simple shock fix is presented to cure the numerical shock instability associated with the ``carbuncle phenomenon' and an entropy fix to remove an expansion shock or glitch at the sonic point. Extensive numerical experiments were conducted to validate the proposed scheme for a wide range of problems, and the results are compiled for comparison with several recent upwind methods.
ISSN:1064-8275
1095-7197
DOI:10.1137/S1064827595287626