An iterative Riemann solver for relativistic hydrodynamics

SIAM Journal on Scientific Computing

Volumn 18, Issue 4, 1997, Pages 982-995

  Dai, Wenlong ^a   Woodward, Paul R ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Godunov scheme; Relativistic flows; Riemann problem; Shock

Indexed keywords

GODUNOV SCHEME; RELATIVISTIC FLOW; RIEMANN PROBLEM;

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; HYDRODYNAMICS; SHOCK WAVES;

ITERATIVE METHODS;

EID: 0031173526     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827595282234     Document Type: Article

References (23)

1. J.F. HAWLEY, L.L. SMARR, AND J.R. WILSON, A numerical study of nonspherical black hole accretion, I. Equations and test problems, Astrophysical J., 277 (1984), pp. 296-311.
2. J.F. HAWLEY, L.L. SMARR, AND J.R. WILSON, A numerical study of nonspherical black hole accretion, II. Finite differencing and code calibration, Astrophysical J. Supp., 55 (1984), pp. 211-246.
3. M.L. NORMAN AND K.-H. WINKLER, Why ultrarelativistic numerical hydrodynamics is difficult, in Astrophysical Radiation Hydrodynamics, K.-H. Winkler and M.L. Norman, eds., Kluwer Academic Publishers, Norwell, MA, 1986, pp. 449-475.
4. S.K. GODUNOV, A difference method for the numerical calculation of discontinuous solutions of the equation of hydrodynamics, Math. Sb., 47 (1959), pp. 271-306.
5. B. VAN LEER, Toward the ultimate conservative difference scheme, V. A second-order sequel to Godunov's method, J. Comput. Phys., 32 (1979), pp. 101-136.
6. P.L. ROE, Approximate Riemann solvers, parameters vectors, and difference schemes, J. Comput. Phys., 43 (1981), pp. 357-372.
7. P.R. WOODWARD AND P. COLELLA, The numerical simulation of two-dimensional fluid flow with strong shock, J. Comput. Phys., 54 (1984), pp. 115-173.
8. P. COLELLA AND P.R. WOODWARD, The piecewise parabolic method (PPM) for gas-dynamical simulations, J. Comput. Phys., 54 (1984), pp. 174-201.
9. A. HARTEN, High resolution schemes for hyperbolic conservation laws, J. Comput. Phys., 49 (1983), pp. 357-393.
10. A. HARTEN, S. OSHER, B. ENGQUIST, AND S. CHAKRAVARTHY, Some results on uniformly high-order accurate essentially nonoscillatory schemes, Appl. Numer. Math., 2 (1986), pp. 347-377.
11. A. HARTEN AND S. OSHER, Uniformly high-order accurate nonoscillatory schemes, I, SIAM J. Numer. Anal., 24 (1987), pp. 279-309.
12. A. HARTEN, B. ENGQUIST, S. OSHER, AND S. CHAKRAVARTHY, Uniformly high-order accurate nonoscillatory schemes, III, J. Comput. Phys., 71 (1987), pp. 231-303.
13. A.M. ANILE, Relativistic Fluids and Magnetofluids, Cambridge University Press, London, 1989.
14. K.W. THOMPSON, The special relativistic shock tube, J. Fluid Mech., 171 (1986), pp. 365-375.
15. J.A. FONT, J.M. IBANEZ, A. MARQUINA, AND J.M. MARTI, Multidimensional relativistic hydrodynamics: Characteristic fields and modern high-resolution shock-capturing schemes, Astron. Astrophys., 282 (1994), pp. 304-314.
16. J.M. MARTI AND E. MULLER, The analytical solution of the Riemann problem in relativistic hydrodynamics, J. Fluid Mech., 258 (1994), pp. 317-333.
17. D.S. BALSARA, Riemann solver for relativistic hydrodynamics, J. Comput. Phys., 114 (1994), pp. 284-297.
18. C.W. MISNER, K.S. THORNE, AND J.A. WHEELER, Gravitation, Freeman Press, San Francisco, 1973.
19. L.D. LANDAU AND E.M. LIFSHITZ, Fluid Mechanics, Pergamon Press, New York, 1987.
20. A.M. TAUB, Relativistic Rankine-Hugoniot equations, Phys. Rev. Ser., 74 (1948), pp. 328-334.
21. W. ISRAEL, Relativistic theory of shock waves, Proc. Roy. Soc. London Ser. A, 259 (1960), pp. 129-143.
22. A. LICHNEROWICZ, Relativistic hydrodynamics and magnetohydrodynamics, Benjamin, New York, 1967.
23. R. COURANT AND K.O. FRIEDRICHS, Supersonic Flow and Shock Wave, 5th ed., Interscience, New York, 1967.