An adaptive Riemann solver using a two-shock approximation

Computers and Fluids

Volumn 28, Issue 6, 1999, Pages 741-777

  Rider, W J ^a  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF STATE; FUNCTIONS; PROBLEM SOLVING; VELOCITY;

ADAPTIVE RIEMANN SOLVER; TAYLOR EXPANSION; TWO SHOCK APPROXIMATION;

APPROXIMATION THEORY;

MATHEMATICAL ANALYSIS; PARTICLE DISPERSION; SHOCK WAVE;

EID: 0033166006     PISSN: 00457930     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7930(98)00033-4     Document Type: Article

References (36)

1. Batten P., Clarke N., Lambert C., Causon D.M. On the choice of wavespeeds for the HLLC Riemann solver. SIAM Journal on Scientific Computing. 18:1997;70-1553.
2. Bell J.B., Colella P., Trangenstein J.A. High order Godunov methods for general systems of hyperbolic conservation laws. Journal of Computational Physics. 82:1989;97-362.
3. Bogdanoff D.W., Brackett D.C. Godunov computational fluid dynamics method for extreme flow velocities and any equation of state. AIAA Journal. 27:1989;17-909.
4. Colella P. Glimm's method for gas dynamics. SIAM Journal on Scientific and Statistical Computing. 3:1982;76-110.
5. Colella P., Glaz H.M. Efficient solution algorithms for the Riemann problem in real gases. Journal of Computational Physics. 58:1985;89-264.
6. Courant R., Friedrichs K.O. Supersonic flow and shock waves. New York: Interscience, 1948.
7. Davis S.F. Simplified second-order Godunov-type methods. SIAM Journal on Scientific and Statistical Computing. 9:1988;73-445.
8. Dukowicz J.K. A general non-iterative Riemann solver for Godunov's method. Journal of Computational Physics. 61:1986;37-119.
9. Einfeldt B. On Godunov-type methods for gas dynamics. SIAM Journal on Numerical Analysis. 25:1988;294-318.
10. Einfeldt B., Munz C.D., Roe P.L., Sjögreen B. On Godunov-type methods near low densities. Journal of Computational Physics. 92:1991;95-273.
11. Engquist B., Osher S. One-sided difference approximations for nonlinear conservation laws. Mathematics of Computation. 36:1981;51-321.
12. Godunov S.K. Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics. Matematicheski Sbornik. 47:1959;271-306.
13. Godunov S.K., Zabrodyn A.W., Prokopov G.P. A computational scheme for two-dimensional nonstationary problems of gas dynamics and calculation of the flow from a shock wave approaching steady-state. USSR Journal of Computational Mathematics and Mathematical Physics. 1:1961;219-1187.
14. Gottlieb J.J., Groth C.P.T. Assessment of Riemann solvers for unsteady one-dimensional inviscid flows of perfect gases. Journal of Computational Physics. 78:1988;58-437.
15. Isaacson E.L, Marchesin D., Palmeira C.F., Plohr B.J. A global formalism for nonlinear waves in conservation laws. Communications in Mathematical Physics. 146:1992;52-505.
16. Lax PD. Hyperbolic systems of conservation laws and the mathematical theory of shock waves. Philadelphia: SIAM, 1972.
17. McQueen RG. Shock waves in condensed media: their properties and the equations of state of materials derived from them. In: Eliezer S., Ricci R.A., editors. High-pressure equations of state: theory and applications. Varenna on Lake Como, Villa Monastero, Italy. North-Holland: 1989.
18. Menikoff R., Plohr B.J. The Riemann problem for fluid flow of real materials. Reviews in Modern Physics. 61:1989;75-129.
19. Miller G.H., Puckett E.G. A high-order Godunov method for multiple condensed phases. Journal of Computational Physics. 128:1996;64-134.
20. Munz C.D. On Godunov-type schemes for Lagrangian gas dynamics. SIAM Journal on Numerical Analysis. 31:1994;17-42.
21. Noh W.F. Errors for calculations of strong shocks using an artificial viscosity and an artificial heat flux. Journal of Computational Physics. 72:1987;78-120.
22. Quirk J.J. A contribution to the great Riemann solver debate. International Journal for Numerical Methods in Fluids. 18:1992;74-555.
23. Roe P.L. Approximate Riemann solvers, parameter vectors, and difference schemes. Journal of Computational Physics. 43:1981;72-357.
24. Ruoff A.L. Linear shock-velocity-particle-velocity relationship. Journal of Applied Physics. 38:1967;80-497.
25. Segletes S.B. Thermodynamic stability of the Mie-Grüneisen equation of state, and its relevance to hydrocode computations. Journal of Applied Physics. 70:1991;99-2489.
26. Segletes S.B. Further examination on the thermodynamic stability of the Mie-Grüneisen equation of state. Journal of Applied Physics. 76:1994;66-4560.
27. Sod G. A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws. Journal of Computational Physics. 27:1978;1-31.
28. Thompson P.A. A fundamental derivative in gas dynamics. Physics of Fluids. 14:1971;9-1843.
29. Toro EF. Riemann solvers and numerical methods for fluid dynamics. Berlin: Springer, 1997.
30. Toro E.F., Spruce M., Speares W. Restoration of the contact surface in the HLL-Riemann solver. Shock Waves. 4:1994;25-34.
31. van Albada G.D., van Leer B., Roberts W.W. A comparative study of computational methods in cosmic gas dynamics. Astronomy and Astrophysics. 108:1982;76-84.
32. van Leer B. Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection. Journal of Computational Physics. 23:1977;99-276.
33. van Leer B. On the relation between the upwind-differencing schemes of Godunov, Engquist-Osher and Roe. SIAM Journal on Scientific and Statistical Computing. 5:1984;1-20.
34. Whalen P. Personal communication.
35. Wilkins M.L. Use of artificial viscosity in multidimensional fluid dynamic calculations. Journal of Computational Physics. 36:1980;281-303.
36. Woodward P., Colella P. The numerical simulation of two-dimensional fluid flow with strong shocks. Journal of Computational Physics. 54:1984;73-115.