×

zbMATH — the first resource for mathematics

Methods for the accurate computations of hypersonic flows. I: AUSMPW+scheme. (English) Zbl 1106.76421
Summary: In order to overcome some difficulties observed in the computation of hypersonic flows, a robust, accurate and efficient numerical scheme based on AUSM-type splitting is developed. Typical symptoms appearing in the application of AUSM-type schemes for high-speed flows, such as pressure wiggles near a wall and overshoots across a strong shock, are cured by introducing weighting functions based on pressure (AUSMPW). A newly improved version of the AUSMPW scheme, called AUSMPW+, is developed to increase the accuracy and computational efficiency of AUSMPW in capturing an oblique shock without compromising robustness. With a new definition of the numerical speed of sound at a cell interface, capturing an oblique shock is remarkably enhanced, and it can be proved that an unphysical expansion shock is completely excluded. With simple Mach number interpolation functions, AUSMPW+ is efficient to implement. Extensive numerical tests from supersonic frozen flows to hypersonic nonequilibrium flows validate that the AUSMPW+ scheme provides accurate solutions for the computation of high-speed flows.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76K05 Hypersonic flows
76L05 Shock waves and blast waves in fluid mechanics
76V05 Reaction effects in flows
Software:
AUSM; AUSMPW+
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] C. Park, Interaction of Spalled Particles with Shock Layer Flow, AIAA Paper 99-0353, AIAA Press, Washington, DC, 1999.
[2] Steger, J.L; Warming, R.F, Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods, J. comput. phys., 40, 263, (1981) · Zbl 0468.76066
[3] Van Leer, B, Flux-vector splitting for the Euler equation, Lecture notes phys., 170, 507, (1982)
[4] Gressier, J; Villedieu, P; Moshetta, J.-M, Positivity of flux vector splitting schemes, J. comput. phys., 155, 199, (1999) · Zbl 0953.76064
[5] Roe, P.L, Approximate Riemann solvers, parameter vectors and difference schemes, J. comput. phys., 43, 357, (1981) · Zbl 0474.65066
[6] Quirk, J.J, A contribution to the great Riemann solver debate, Int. J. numer. meth. fluids, 18, 555, (1994) · Zbl 0794.76061
[7] Einfeldt, B, On Godunov-type method for gas dynamics, SIAM J. numer anal., 25, 294, (1988) · Zbl 0642.76088
[8] Liou, M.S; Steffen, C.J, A new flux splitting scheme, J. comput. phys., 107, 23, (1993) · Zbl 0779.76056
[9] M. S. Liou, and, Y. Wada, A Flux Splitting Scheme with High-Resolution and Robustness for Discontinuities, AIAA Paper 94-0083, AIAA Press, Washington, DC, 1994.
[10] Liou, M.S, A sequel to AUSM: AUSM+, J. comput. phys., 129, 364, (1996) · Zbl 0870.76049
[11] Kim, K.H; Rho, O.H, An improvement of AUSM schemes by introducing the pressure-based weight functions, Comput. fluids, 27, 311, (1998) · Zbl 0964.76064
[12] Kim, K.H; Rho, O.H, An improvement of AUSM schemes by introducing the pressure-based weight functions, The fifth annual conference of the computational fluid dynamics society of Canada (CFD 97), 5, 14.33-14.38, (1997)
[13] J. R. Edwards, A Low-Diffusion Flux-Splitting Scheme for Navier-Stokes Calculations, AIAA Paper 95- 1703-CP, AIAA Press, Washington, DC, 1995.
[14] S. Srinivasan, J. C. Tannehill, and, K. J. Weilmuenster, Simplified Curve Fits for the Thermodynamic Properties of Equilibrium Air, NASA RP-1181, Aug. 1987.
[15] R. N. Gupta, K. P. Lee, R. A. Thompson, and, J. M. Yos, Calculations and Curve Fits of Thermodynamic and Transport Properties for Equilibrium Air to 30000 K, NASA RP-1260, 1991.
[16] Murthy, T.K.S, computational methods in hypersonic aerodynamics, (1991), Kluwer Academic Dordrecht · Zbl 0777.00022
[17] Park, C, Review of chemical-kinetic problems of future NASA missions, I: Earth entries, J. thermophys. heat transf., 7, 385, (1993)
[18] Liou, M.S, Mass flux schemes and connection to shock instability, J. comput. phys., 160, 623, (2000) · Zbl 0967.76062
[19] Tatsumi, S; Martinelli, L; Jameson, A, Design, implementation and validation of flux limited schemes for the solution of the compressible navier – stokes equations, Aiaa j., 33, 252, (1995) · Zbl 0824.76058
[20] Reference deleted in proof.
[21] Reference deleted in proof.
[22] Reference deleted in proof.
[23] Reference deleted in proof.
[24] Reference deleted in proof.
[25] Reference deleted in proof.
[26] Reference deleted in proof.
[27] Reference deleted in proof.
[28] Reference deleted in proof.
[29] Reference deleted in proof.
[30] Reference deleted in proof.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.