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Tenaud, C.; Garnier, E.; Sagaut, P.

Evaluation of some high-order shock capturing schemes for direct numerical simulation of unsteady two-dimensional free flows. (English) Zbl 0977.76065

Int. J. Numer. Methods Fluids 33, No. 2, 249-278 (2000).
The paper examines the efficiency and performance of some shock-capturing schemes as possible candidates for direct numerical simulation tools. These are TVD, MUSCL, compact and ENO schemes applied to unsteady compressible Navier-Stokes equations in Cartesian coordinates. The schemes are tested on the advection of a vortex in uniform free flow, on the interaction between a temperature spot and a weak shock, and on the interaction of Taylor vortex with weak shock. The solutions obtained with a sixth-order compact scheme on the \(800\times 100\) mesh are considered as reference ones. It is found that ENO schemes demonstrate the best agreement with the reference solutions.
Reviewer: A.I.Tolstykh (Moskva)

Cited in 15 Documents

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
76L05 Shock waves and blast waves in fluid mechanics

Keywords:

unsteady compressible Navier-Stokes equations; high-order shock-capturing schemes; TVD schemes; MUSCL schemes; compact schemes; Cartesian coordinates; advection of vortex; temperature spot; weak shock; Taylor vortex; ENO schemes
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References:

[1] Moin, Annual Review in Fluid Mechanics 30 pp 539– (1998)
[2] Lee, Journal of Fluid Mechanics 251 pp 533– (1993)
[3] Kovasznay, Journal of Aerospace Science 20 pp 657– (1953)
[4] Ribner, AIAA Journal 23 pp 1708– (1985)
[5] Shu, Journal of Computational Physics 77 pp 439– (1988)
[6] Roe, Journal of Computational Physics 43 pp 357– (1981)
[7] Harten, Journal of Computational Physics 49 pp 357– (1996)
[8] Yee, AIAA Journal 25 pp 266– (1987)
[9] Picone, Journal of Fluid Mechanics 189 pp 23– (1988)
[10] Numerical experiments with s symmetric high resolution shock-capturing scheme. NASA TM-88325, 1986.
[11] Explicit and implicit compact high resolution shock-capturing methods for multidimensional Euler equations I: formulation. NASA TM-110364, 1995.
[12] On the implementation of a class of upwind schemes for system of hyperbolic conservation laws, NASA TM-86839, 1985.
[13] Shu, Journal of Computational Physics 83 pp 32– (1989)
[14] Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. NASA/CR-97-206253 and ICASE Report 97-65, 1995.
[15] Shu, Journal of Scientific Computing 5 pp 127– (1990)
[16] Jiang, Journal of Computational Physics 126 pp 202– (1996)
[17] Poursuite du d?velopment du code PEGASE en simulation en compressible. Rapport Technique de Synth?se ONERA RTS 20/4368 DSNA/Y, 1998.
[18] Theory of vorticity generation by shock wave and flame interactions. In Dynamics of Shock Waves?Explosions and Detonations, 94, Progress in Astronautics and Aeronautics, (eds). 1983.
[19] M?thodes d’Ordre Elev? Appliqu?es au Calcul d’Ecoulements de Fluides Compressibles. Th?se de Doctorat de l’Universit? Paris VI, 1988.
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