Uniqueness conditions for Riemann problems of ideal magnetohydrodynamics

Journal of Plasma Physics

Volumn 69, Issue 3, 2003, Pages 253-276

  Torrilhon, M ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

GAS DYNAMICS; MAGNETIC FIELDS; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS; PLASMA FLOW; PROBLEM SOLVING; SHOCK WAVES;

NON-STRICT HYPERBOLIC SYSTEMS; ONE-DIMENSIONAL PROCESSES; RAREFACTION FANS;

MAGNETOHYDRODYNAMICS;

EID: 0242718378     PISSN: 00223778     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022377803002186     Document Type: Article

References (23)

1. Landau, L. D. and Lifshitz, E. M. 1960 Electrodynamic of Continuous Media, Course in Theoretical Physics, Vol. 8. Oxford: Pergamon.
2. Serre, D. 1999 Systems of Conservation Laws, Vol. 1. Cambridge: Cambridge University Press.
3. Jeffrey, A. and Taniuti. T. 1964 Non-linear Wave Propagation. New York: Academic.
4. [41 Liberman, M. A. and Velikovich, A. L. 1986 Physics of Shock Waves in Gases and Plasmas, Springer Series in Electrophysics, Vol. 19. Berlin: Springer-Verlag.
5. Brio, M. and Wu, C. C. 1988 An upwind differencing scheme for the equations of ideal magnetohydrodynamics. J. Comp. Phys. 75, 400.
6. Wu, C.C. 1990 Formation, structure, and stability of MHD intermediate shocks. J. Geophys. Res. (Space Phya.) 95/6, 8149.
7. Wu, C. C. 1995 Magnetohydrodynamic Riemann problem and the structure of the magnetic reconnection layer. J. Geophys. Res. (Space Phys.) 100/4, 5579.
8. DeSterck, H. and Poedts, S. 2000 Intermediate shocks in three-dimensional magnetohydrodynamic bow-shock flows with multiple interacting shock fronts. Phys. Rev. Lett. 84, 5524.
9. DeSterck, H. and Poedts, S. 2001 Disintegration and reformation of intermediate shock segments in three-dimensional MHD bow shook flows. J. Geophys. Res. 106.
10. Freistühler, H. and Szmolyan, P. 1995 Existence and bifurcation of viscous profiles for all intermediate magnetohydrodynamic shock waves. SIAM J. Math. Anal. 26, 112.
11. Freistühler, H. and Rohde, C. 1999 Numerical methods for viscous profiles of nonclassical shock waves. Proc. 7th Int. Conf. Hyp. Problems, Int. Series of Num. Math., Vol. 129. Basel: Birkhäuser.
12. Myong, R. S. and Roe, P. L. 1997 Shock waves and rarefaction waves in magnetohydrodynamics. Part 1. A model system. J. Plasma Phys. 58, 485.
13. Myong, R.S. and Roe, PL. 1997 Shock waves and rarefaction waves in magnetohy-drodynamics. Part 2. The MHD system. J. Plasma Phys. 58, 521.
14. Falle, S. A. E. G. and Komissarov, S. S. 2001 On the inadmissibility of non-evolutionary shocks. J. Plasma Phys. 65, 29.
15. LeVeque, R. J. 1992 Numerical Methods for Conservation Laws, 2nd edn, Lectures in Mathematics. Basel: Birkhäuser.
16. Toro, E. F. 1999 Riemann Solvers and Numerical Methods for Fluid Dynamics, 2nd edn. Berlin: Springer-Verlag.
17. Lax, P.D. 1957 Hyperbolic systems of conservation laws II. Comm. Pure Appl. Math. 10, 537.
18. Barmin, A. A., Kulikovskiy, A.G. and Pogorelov, N. V. 1996 Shock-capturing approach and nonevolutionary solutions in magnetohydrodynamics. J. Comp. Phys. 126, 77.
19. Dai, W. and Woodward, P.R. 1994 An approximate Riemann solver for ideal magnetohydrodynamics. J. Comp. Phys. 111, 354.
20. Bazer, J. and Ericson, W. B. 1958 Hydromagnetic shocks. Astrophys. J. 129, 758.
21. Ericson, W. B. and Bazer, J. 1960 On certain properties of hydromagnetic shocks. Phys. Fluids 3, 631.
22. Ryu, D. and Jones, T. W. 1995 Numerical magnetohydrodynamics in astrophysics: algorithm and tests for one-dimensional flow. Astrophys. J. 442, 228.
23. Torrilhon, M. 2002 Exact Solver and Uniqueness Conditions for Riemann Problems of Ideal Magnetohydrodynamics, research report 2002-06. Zurich: Seminar for Applied Mathematics, ETH.