A high-order Godunov-type scheme for shock interactions in ideal magnetohydrodynamics

SIAM Journal on Scientific Computing

Volumn 18, Issue 4, 1997, Pages 957-981

  Dai, Wenlong ^a   Woodward, Paul R ^b  

^a University of Minnesota   (United States)

^b UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Finite difference methods; Godunov type method; Hyperbolic conservation laws; MHD shocks; Riemann problems

Indexed keywords

GODUNOV TYPE METHOD; HYPERBOLIC CONSERVATION LAWS; NONLINEAR RIEMANN SOLVER; PIECEWISE PARABOLIC METHOD;

COMPUTER SIMULATION; FINITE DIFFERENCE METHOD; MAGNETOHYDRODYNAMICS; NONLINEAR EQUATIONS; SHOCK TUBES; SHOCK WAVES;

COMPUTATIONAL METHODS;

EID: 0031173525     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827593257729     Document Type: Article

References (27)

1. P. D. LAX, Weak solutions of nonlinear hyperbolic equations and their numerical computation, Comm. Pure Appl. Math., VII (1954), pp. 159-193.
2. S. K. GODUNOV, Difference methods for the numerical calculation of the equations of fluid dynamics, Math. Sb., 47 (1959), pp. 271-306. (In Russian.)
3. P. D. LAX, Hyperbolic Systems of Conservation Laws and Mathematical Theory of Shock Waves, SIAM, Philadelphia, PA, 1973.
4. B. VAN LEER, Toward the ultimate conservative difference scheme II. Monotonicity and conservation combined in a second order scheme, J. Comput. Phys., 14 (1974), pp. 361-370.
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. J. GLIMM, E. ISAACSON, D. MARCHESIN, AND O. MCBRYAN, Front tracking for hyperbolic system, Adv. in Appl. Math., 2 (1981), pp. 91-119.
7. P. L. ROE, Approximate Riemann solvers, parameters vectors, and difference schemes, J. Comput. Phys., 43 (1981), pp. 358-372.
8. B. ENGQUIST AND S. OSHER, One-sided difference approximations for nonlinear conservation laws, Math. Comput., 36 (1981), pp. 321-351.
9. S. OSHER AND F. SOLOMON, Upwind difference schemes for hyperbolic systems of conservation law, Math. Comput., 38 (1983), pp. 339-374.
10. A. HARTEN, High resolution schemes for hyperbolic conservation laws, J. Comput. Phys., 49 (1983), pp. 357-393.
11. 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.
12. P. COLELLA AND P. R. WOODWARD, The piecewise parabolic method (PPM) for gas dynamical simulations, J. Comput. Phys., 54 (1984), pp. 174-201.
13. H. C. YEE, R. F. WARMING, AND A. HARTEN, Implicit total variation diminishing (TVD) scheme for steady state calculations, J. Comput. Phys., 57 (1985), pp. 327-360.
14. I. L. CHERN, J. GLIMM, O. MCBRYAN, B. PLOHR, AND S. YANIV, Front tracking for gas dynamics, J. Comput. Phys., 62 (1986), pp. 83-110.
15. P. R. WOODWARD, Piecewise parabolic methods for astrophysical fluid dynamics, in Astrophysical Radiation Hydrodynamics, K.-H. A. Winkler and M. L. Norman, eds., D. Reidel, Boston, MA, 1986, pp. 245-326.
16. A. T. GIZ, Parker Instability in Interstellar Medium With a Realistic Gravitational Field and a Computer Code for Magnetohydrodynamics, Ph.D. thesis, Department of Astronomy, University of California, Berkeley, CA, 1987.
17. M. BRIO AND C. C. Wu, An upwind differencing scheme for the equations of ideal magnetohydrodynamics, J. Comput. Phys., 75 (1988), pp. 400-422.
18. A. L. ZACHARY AND P. COLELLA, A high-order Godunov method for the equations of ideal magnetohydrodynamics, J. Comput. Phys., 99 (1992), pp. 341-347.
19. A. L. ZACHARY, A. MALAGOLI, AND P. COLELLA, A higher-order Godunov method for multidimensional ideal magnetohydrodynamics, SIAM J. Sci. Comput., 15 (1994), pp. 263-284.
20. J. B. BELL, P. COLELLA, AND J. A. TRANGENSTEIN, Higher order Godunov methods for general systems of hyperbolic conservation laws, J. Comput. Phys., 82 (1989), pp. 362-397.
21. M. BRIO, Admissibility conditions for weak solutions of nonstrictly hyperbolic systems, in Non-linear Hyperbolic Equations - Theory, Computation Methods, and Applications, Proc. Second International Conference on Nonlinear Hyperbolic Problems, Aachen, FRG, 1988.
22. J. GLIMM, Nonuniqueness of solutions for Riemann problems, in Nonlinear Hyperbolic Equations - Theory, Computation Methods, and Applications, Proc. Second International Conference on Nonlinear Hyperbolic Problems, Aachen, FRG, 1988.
23. R. COURANT AND K. O. FRIEDRICHS, Supersonic Flow and Shock Wave, 5th ed., Interscience, New York, 1967.
24. L. D. LANDAU AND E. M. LIFSHITZ, Electrodynamics of Continuous Media, Pergamon Press, New York, 1960.
25. A. JEFFREY AND T. TANIUTI, Non-Linear Wave Propagation, Academic Press, New York, 1964.
26. A. G. KULIKOVSKIY AND G. A. LYUBIMOV, Magnetohydrodynamics, Addison-Wesley, Reading, MA, 1965.
27. A. R. KANTROWITZ AND H. E. PETSCHECK, Plasma Physics in Theory and Application, McGraw-Hill, New York, 1966.