Non-oscillatory central schemes for one- and two-dimensional MHD equations: I

Journal of Computational Physics

Volumn 201, Issue 1, 2004, Pages 261-285

  Balbás, Jorge ^a   Tadmor, Eitan ^b   Wu, Cheng Chin ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF MARYLAND   (United States)

Author keywords

High resolution central schemes; Ideal magnetohydrodynamics (MHD) equations; Jacobian free form; Multidimensional conservation laws; Non oscillatory reconstructions

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; SHOCK TUBES;

CENTRAL SCHEME; HIGH-RESOLUTION CENTRAL SCHEMES; IDEAL MAGNETOHYDRODYNAMICS EQUATIONS; JACOBIAN FREE FORM; JACOBIANS; MAGNETOHYDRODYNAMIC EQUATIONS; MULTIDIMENSIONAL CONSERVATION LAWS; NON-OSCILLATORY RECONSTRUCTION; ONE-DIMENSIONAL; TWO-DIMENSIONAL;

MAGNETOHYDRODYNAMICS;

EID: 13844251984     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2004.05.020     Document Type: Article

References (27)

1. J. Adams, P. Swarztrauber, R. Sweet, Fishpack. Available from
2. J.U. Brackbill J.C. Barnes The effect of Nonzero div B on the numerical solution of the magnetohydrodynamic equations J. Comput. Phys. 35 1980 426
3. M. Brio C.C. Wu An upwind differencing scheme for the equations of magnetohydrodynamics J. Comput. Phys. 75 2 1988 400-422
4. F. Bianco G. Puppo G. Russo High order central schemes for hyperbolic systems of conservation laws SIAM J. Sci. Comput. 21 1 1999 294-322
5. R.B. Dahlburg J.M. Picone Evolution of the Orszag-Tang vortex system in a compressible medium. I. Initial average subsonic flow Phys. Fluids B 1 1989 2153
6. W. Dai P.R. Woodward A simple finite difference scheme for multidimensional magnetohydrodynamical equations J. Comput. Phys. 142 1998 331-369
7. L. Del Zanna N. Bucciantini P. Londrillo A third order shock-capturing code for relativistic 3-D MHD Mem. Soc. Astron. Italiana 1 2002
8. L. Del Zanna N. Bucciantini P. Londrillo An efficient shock-capturing central-type scheme for multidimensional relativistic flows II Astron. Astrophys. 400 2003 397-413
9. B. Engquist O. Runborg Multi-phase computations in geometrical optics J. Comput. Appl. Math. 74 1996 175-192
10. A. Harten B. Engquist S. Osher S.R. Chakravarthy Uniformly high order accurate essentially non-oscillatory schemes III J. Comput. Phys. 71 1987 231-303
11. D.R. van der Heul C. Vuik P. Wesseling A conservative pressure-correction method for the Euler and ideal MHD equations at all speeds Int. J. Numer. Meth. Fluids 40 2002 521-529
12. G.-S. Jiang E. Tadmor Nonoscillatory central schemes for multidimensional hyperbolic conservation laws SIAM J. Sci Comput. 19 6 1998 1892-1917
13. G.-S. Jiang C.C. Wu A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics J. Comput. Phys. 150 1999 561-594
14. S. Jin Z.-P. Xin Numerical passage from systems of conservation Laws to Hamilton-Jacobi equations and relaxation schemes SIAM J. Numer. Anal. 35 1994 2385-2404
15. A. Kurganov E. Tadmor New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations J. Comput. Phys. 160 2000 214-282
16. A. Kurganov S. Noelle G. Petrova Semi-discrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations SIAM J. Sci. Comput. 23 2000 707-740
17. B. van Leer Towards the ultimate conservative difference scheme V. A second order sequel to Godunov's method J. Comput. Phys. 32 1979 101-136
18. D. Levy G. Puppo G. Russo A fourth order central WENO scheme for multidimensional hyperbolic systems of conservation laws SIAM J. Sci. Comput. 24 2002 480-506
19. X.-D. Liu E. Tadmor Third order nonoscillatory central scheme for hyperbolic conservation laws Numer. Math. 79 1998 397-425
20. X.-D. Liu S. Osher Nonoscillatory third order accurate self-similar maximum principle satisfying shock capturing schemes. I Sinum 33 1996 760-779
21. H. Nessayahu E. Tadmor Non-oscillatory central differencing for hyperbolic conservation laws J. Comput. Phys. 87 2 1990 408-463
22. S.A. Orszag C.M. Tang Small-scale structure of two-dimensional magnetohydrodynamic turbulence J. Fluid Mech. 90 1979 129
23. J.M. Picone R.B. Dahlburg Evolution of the Orszag-Tang vortex system in a compressible medium II. Supersonic flow Phys. Fluids B 3 1991 29
24. K.G. Powell, P.L. Roe, R.S. Myong, T. Gombosi, D. deZeeuw, An upwind scheme for magnetohydrodynamics, in: AIAA 12th Computational Fluid Dynamics Conference, San Diego, CA, June 19-22, 1995, pp. 661-674
25. H.-Z. Tang K. Xu A high-order gas-kinetic method for multidimensional ideal magnetohydrodynamics J. Comput. Phys. 65 2000 69-88
26. C.C. Wu Formation, structure, and stability of MHD intermediate shocks J. Geophys. Res. 95 A6 1990 8149-8175
27. C.C. Wu T. Chang Further study of the dynamics of two-dimensional MHD coherent structures - A large scale simulation J. Atmos. Solar Terrestr. Phys. 95 2001 1447-1453