Mass Flux Schemes and Connection to Shock Instability

Journal of Computational Physics

Volumn 160, Issue 2, 2000, Pages 623-648

  Liou, Meng Sing ^a  

^a NASA GLENN RESEARCH CENTER   (United States)

Author keywords

AUSM schemes; Mass flux; Shock (carbuncle) instability; Upwind methods

Indexed keywords

AERODYNAMICS; MACH NUMBER;

AUSM + SCHEME; CONSERVATION EQUATIONS; CONTACT DISCONTINUITIES; LIMITING CASE; MOVING DISCONTINUITIES; NUMERICAL FLUX; SHOCK (CARBUNCLE) INSTABILITY; SHOCK INSTABILITIES; STATIONARY DISCONTINUITY; UPWIND METHOD;

BOUNDARY LAYERS;

EID: 0000104186     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2000.6478     Document Type: Article

References (22)

1. S. K. Godunov, A difference method for the numerical calculation of discontinuous solutions of hydrodynamic equations, Mat. Sb. 47, 271, 1959, (translation, US JPRS: 7225, November 1960, ).
2. Wada Y., Liou M.-S. An accurate and robust flux splitting scheme for shock and contact discontinuities. SIAM J. Sci. Comput. 18:1997;633.
3. M.-S. Liou, Probing numerical fluxes: Mass flux, positivity, and entropy-satisfying property, AIAA paper 97-2035-CP, 1997.
4. Roe P. L. Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43:1981;357.
5. Osher S., Solomon F. Upwind difference schemes for hyperbolic systems of conservation laws. Math. Comp. 38:1982;339.
6. van Leer B. Flux-vector splitting for the Euler equations, in Lecture Notes in Physics. 1982;Springer-Verlag, Berlin. p. 507.
7. D. Hänel, R. Schwane, and, G. Seider, On the accuracy of upwind schemes for the solution of the Navier-Stokes equations, AIAA paper 87-1105-CP, 1987.
8. Einfeldt B. On Godunov-type methods for gas-dynamics. SIAM J. Numer. Anal. 25:1988;294.
9. Einfeldt B., Munz C. D., Roe P. L., Sjögreen B. On Godunov-type methods near low densities. J. Comput. Phys. 92:1991;273.
10. Obayashi S., Wada Y. Practical formulation of a positively conservative scheme. AIAA J. 32:1994;1093.
11. +. J. Comput. Phys. 129:1996;364.
12. Liou M.-S., Steffen C. J. A new flux splitting scheme. J. Comput. Phys. 107:1993;23.
13. Quirk J. J. A contribution to the great Riemann solver debate. Internat. J. Numer. Methods Fluids. 18:1994;555.
14. F. Coquel, and, M.-S. Liou, Hybrid upwind splitting (HUS) by a field-by-field decomposition, NASA TM 106843, 1995.
15. E. Shima, and, T. Jounouchi, AUSM type upwind schemes, preprint, 1996.
16. Swanson R. C., Radespiel R., Turkel E. On some numerical dissipation schemes. J. Comput. Phys. 147:1998;518.
17. K. M. Peery, and, S. T. Imlay, Blunt-body flow simulations, in, AIAA/SAE/ASME/ASEE 24th Joint Propulsion Conference, 1988; AIAA paper 88-2904.
18. H.-C. Lin, Dissipation additions to flux-difference splitting, in, 10th AIAA Computational Fluid Dynamics Conference, 1991; AIAA paper 91-1544.
19. Edwards J. R. A low-diffusion flux-splitting scheme for Navier-Stokes calculations. Comput. & Fluids. 26:1997;635.
20. Pandolfi M., D'Ambrosio D. Upwind methods and carbuncle phenomenon. Proceedings of the Fourth European Computational Fluid Dynamics Conference. 1998;126.
21. Jameson A. Analysis and design of numerical schemes for gas dynamics. II. Artificial diffusion and discrete shock structure. Internat. J. Comput. Fluid Dynamics. 5:1995;1.
22. Sanders R., Morano E., Druguet M. Multidimensional dissipation for upwind schemes: Stability and applications to gas dynamics. J. Comput. Phys. 145:1998;511.