A sequel to AUSM, Part II: AUSM+-up for all speeds

Journal of Computational Physics

Volumn 214, Issue 1, 2006, Pages 137-170

  Liou, Meng Sing ^a  

^a NASA GLENN RESEARCH CENTER   (United States)

Author keywords

AUSM scheme; AUSM+ up; Carbuncle phenomenon; Entropy satisfying; Euler and Navier Stokes equations; Low Mach number; Positivity; Upwind scheme

Indexed keywords

AERODYNAMICS; ASYMPTOTIC ANALYSIS; MACH NUMBER;

AUSM + SCHEME; AUSM+-UP; CARBUNCLE PHENOMENA; ENTROPY-SATISFYING; EULER AND NAVI-STOKE EQUATION; LOW MACH NUMBERS; NAVIER-STOKES EQUATION; POSITIVITY; THEORETICAL DEVELOPMENT; UP-WIND SCHEME;

NAVIER STOKES EQUATIONS;

EID: 33644550669     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2005.09.020     Document Type: Article

References (40)

1. E. Turkel Preconditioned methods for solving incompressible and low speed compressible equations Journal of Computational Physics 72 1987 277-298
2. Y.H. Choi C.L. Merkle The application of preconditioning in viscous flows Journal of Computational Physics 105 1993 207-223
3. J.M. Weiss, W.A. Smith, Preconditioning applied to variable and constant density time-accurate flows on unstructured meshes, AIAA Paper 94-2209, June 1994.
4. B. van Leer, W.T. Lee, P.L. Roe, Characteristic time stepping or local preconditioning of the Euler equations, in: 10th AIAA CFD Conference, Paper 91-1552-CP, 1991.
5. P.L. Roe Approximate Riemann solvers, parameter vectors, and difference schemes Journal of Computational Physics 43 1981 357-372
6. + and H-CUSP schemes for turbomachinery applications, AIAA Paper 2003-4120-CP, in: 16th AIAA CFD Conference, June 2003.
7. J.R. Edwards M.-S. Liou Low-diffusion flux-splitting methods for flows at all speeds AIAA Journal 36 1998 1610-1617
8. M.-S. Liou, J.R. Edwards, Numerical speed of sound and its application to schemes for all speeds, AIAA Paper 99-3268-CP, in: 14th AIAA CFD Conference, 1999.
9. M.-S. Liou, P.G. Buning, Contribution of the recent AUSM schemes to the OVERFLOW code: Implementation and validation, AIAA Paper 2000-4404, 2000.
10. I. Mary P. Sagaut M. Deville An algorithm for unsteady viscous flows at all speeds International Journal of Numerical Methods in Fluids 34 2000 371-401
11. J.R. Edwards R.K. Franklin M.-S. Liou Low-diffusion flux-splitting methods for real fluid flows at all speeds AIAA Journal 38 2000 1624-1633
12. J. Edwards, D. Mao, Development of low-diffusion flux-splitting methods for dense gas - solid flows, AIAA Paper 2001-2649-CP, 2001.
13. + scheme to compressible two-fluid models Computers & Fluids 32 2003 891-916
14. + scheme, AIAA Paper 2003-4107, 2003.
15. M.-S. Liou C.J. Steffen Jr. A new flux splitting scheme Journal of Computational Physics 107 1993 23-39 Also NASA TM 104404, May 1991
16. + Journal of Computational Physics 129 1996 364-382 Also NASA TM 106524, March 1994
17. + scheme Journal of Computational Physics 174 2001 38-80
18. B. Müller, Low mach number asymptotics of the Navier - Stokes equations and numerical implications, VKI CFD Lecture Series, 1999-03, 1999.
19. R.G. Rehm H.R. Baum The equations of motion for thermally driven Buoyant flows Journal of Research of the National Bureau of Standards 83 1978 297-308
20. M.-S. Liou, Ten years in the making - AUSM-family, AIAA Paper 2001-2521-CP, in: 15th AIAA CFD Conference, June 11-14, 2001.
21. B. Van Leer Flux-vector splitting for the Euler equations Lecture Notes in Physics 170 1982 507-512
22. T.W. Roberts The behavior of flux difference splitting schemes near slowly moving shock waves Journal of Computational Physics 90 1990 141-160
23. S.K. Godunov A difference method for the numerical calculation of discontinuous solutions of hydrodynamic equations Mat. Sb 47 1959 271-306
24. B. Einfeldt On Godunov-type methods for gas dynamics SIAM Journal on Numerical Analysis 25 1988 294-318
25. Y. Wada M.-S. Liou An accurate and robust flux splitting scheme for shock and contact discontinuities SIAM Journal on Scientific and Statistical Computing 18 1997 633-657
26. M.-S. Liou Mass flux schemes and connection to shock instability Journal of Computational Physics 160 2000 623-648
27. J.J. Quirk A contribution to the great Riemann solver debate International Journal of Numerical Methods Fluids 18 1994 555-574 Also ICASE Report 92-64, 1992
28. P.G. Buning, et al., OVERFLOW User's Manual, version 1.8f, Unpublished NASA Report, 1998.
29. R.V. Chima, Calculation of multistage turbomachinery using steady characteristic boundary conditions, AIAA Paper 98-0968. Also NASA TM-1998-206613, 1998.
30. F.R. Mentor Two-equation Eddy-viscosity turbulence models for engineering applications AIAA Journal 32 1994 1598-1605
31. D.C. Wilcox Reassessment of the scale-determining equation for advanced turbulence models AIAA Journal 26 1988 1299-1310
32. P.R. Spalart, S.R. Allmaras, A one-equation turbulence model for aerodynamic flows, AIAA Paper 92-0439, 1992.
33. B. Koren Upwind schemes, multigrid and defect correction for the steady Navier - Stokes equations Lecture Notes in Physics 323 1989 344-348
34. W.D. Bachalo D.A. Johnson Transonic turbulent boundary-layer separation generated on an axisymmetric flow model AIAA Journal 24 1986 437-443
35. + method for all speeds and all grid aspect ratios AIAA Journal 39 2001 2278-2282
36. L.J. Goldman, R.G. Seasholtz, Laser anemometer measurements in an annular cascade of core turbine vanes and comparison with theory, NASA TP 2018, NASA Lewis Research Center, 1982.
37. P.L. Johnson, K.M. Jones, M.D. Madson, Experimental investigation of a simplified 3D high lift configuration in support of CFD validation, AIAA Paper 2000-4217, 2000.
38. A. Jameson, W. Schmidt, E. Turkel, Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time stepping, AIAA Paper 81-1259, 1981.
39. D.A. Treadgold, A.F. Jones, K.H. Wilson, Pressure distribution measurement in the RA 8 ft × 6 ft transonic wind tunnel on RAE wing "A" in combination with an axi-symmetric body at mach numbers of 0.4, 0.8 and 0.9, Appendix B4, AGARD-AR-138, 1984.
40. S.E. Rogers, K. Roth, S.M. Nash, CFD validation of high-lift flows with significant wind-tunnel effects, AIAA Paper 2000-4218-CP, in: AIAA 18th Applied Aerodynamics Conference, Denver, CO, 2000.