High order WENO schemes: Investigations on non-uniform convergence for MHD Riemann problems

Journal of Computational Physics

Volumn 201, Issue 2, 2004, Pages 586-600

  Torrilhon, Manuel ^a   Balsara, D S ^b  

^a ETH ZURICH   (Switzerland)

^b UNIVERSITY OF NOTRE DAME   (United States)

Author keywords

Higher order methods; Hyperbolic partial differential equations; Magnetohydrodynamics; Riemann problem; WENO schemes

Indexed keywords

PARTIAL DIFFERENTIAL EQUATIONS;

ESSENTIALLY NON-OSCILLATORY SCHEMES; HIGH-ORDER; HIGH-ORDER METHODS; HIGHER-ORDER; HIGHER-ORDER METHODS; HYPERBOLIC PARTIAL DIFFERENTIAL EQUATION; NON-UNIFORM; RIEMANN PROBLEM; UNIFORM CONVERGENCE; WEIGHTED ESSENTIALLY NON-OSCILLATORY SCHEME;

MAGNETOHYDRODYNAMICS;

EID: 8744230911     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2004.06.015     Document Type: Article

References (27)

1. D.S. Balsara C.-W. Shu Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy J. Comput. Phys. 160 2000 405-452
2. D.S. Balsara Divergence-free adaptive mesh refinement for magnetohydrodynamics J. Comput. Phys. 174 2001 614
3. D.S. Balsara Second order accurate schemes for magnetohydrodynamics with divergence-free reconstruction Astrophys. J. Suppl. 151 2004 149
4. A.A. Barmin A.G. Kulikovskiy N.V. Pogorelov Shock-capturing approach and non-evolutionary solutions in magnetohydrodynamics J. Comput. Phys. 126 1996 77
5. M. Brio C.C. Wu An upwind differencing scheme for the equations of ideal magnetohydrodynamics J. Comput. Phys. 75 1988 400
6. W. Dai P.R. Woodward An approximate riemann solver for ideal magnetohydrodynamics J. Comput. Phys. 111 1994 354
7. H. De Sterck S. Poedts Intermediate shocks in three-dimensional magnetohydrodynamic bow-shock flows with multiple interacting shock fronts Phys. Rev. Lett. 84/24 2000 5524
8. H. De Sterck S. Poedts Disintegration and reformation of intermediate shock segments in three-dimensional MHD bow shock flows J. Geophys. Res. 106 2001
9. H. De Sterck, S. Poedts, Overcompressive shocks and compound shocks in 2D and 3D magnetohydrodynamic flows, in: Proceedings of the 8th International Conference on Hyperbolic Problems, International Series of Numerical Mathematics, vol. 141, 2001, 791
10. S.A.E.G. Falle S.S. Komissarov On the inadmissibility of non-evolutionary shocks J. Plasma Phys. 65 2001 29
11. H. Freistuhler E.B. Pitman A numerical study of a rotationally degenerate hyperbolic system. part I. The riemann problem J. Comput. Phys. 100 1992 306
12. H. Freistuhler E.B. Pitman A numerical study of a rotationally degenerate hyperbolic system. part II. The cauchy problem SIAM J. Numer. Anal. 32 1995 741
13. A. Jeffrey T. Taniuti Non-linear Wave Propagation 1964 Academic Press New York
14. G.S. Jiang C.-W. Shu Efficient implementation of weighted ENO schemes J. Comput. Phys. 126 1996 202-228
15. G.S. Jiang C.C. Wu A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics J. Comput. Phys. 150 2 1999 561
16. L.D. Landau E.M. Lifshitz Electrodynamic of Continuous Media, Course in Theoretical Physics vol. 8 1960 Pergamon Press Oxford
17. R.J. LeVeque Finite Volume Methods for Hyperbolic Problems 2002 Cambridge University Press Cambridge
18. M.A. Liberman A.L. Velikovich Physics of Shock Waves in Gases and Plasmas, Springer Series in Electrophysics vol. 19 1996 Springer Berlin
19. X.-D. Liu S. Osher T. Chan Weighted essentially non-oscillatory schemes J. Comput. Phys. 115 1994 200
20. R.S. Myong P.L. Roe Shock waves and rarefaction waves in magnetohydrodynamics. Part 1. A model system J. Plasma Phys. 58 3 1997 485
21. R.S. Myong P.L. Roe Shock waves and rarefaction waves in magnetohydrodynamics. Part 2. The MHD system J. Plasma Phys. 58 3 1997 521
22. R.S. Myong P.L. Roe On godunov-type schemes for magnetohydrodynamics, 1. A model system J. Comput. Phys. 147 1998 545-567
23. P.L. Roe D.S. Balsara Notes on the eigensystem of magnetohydrodynamics SIAM J. Num. Anal. 56 1996 57
24. C.-W. Shu S. Osher Efficient implementation of essentially non-oscillatory shock capturing schemes J. Comput. Phys. 77 1988 439
25. M. Torrilhon, Exact Solver for Riemann Problems of Ideal Magnetohydrodynamics, Research Report 2002-06, Seminar for Applied Mathematics, ETH Zurich, 2002
26. M. Torrilhon Uniqueness conditions for Riemann problems of ideal magnetohydrodynamics J. Plasma Phys. 69 3 2003 253
27. M. Torrilhon Non-uniform convergence of finite-volume-schemes for Riemann problems of ideal magnetohydrodynamics J. Comput. Phys. 192 2003 73-94