Nonoscillatory central schemes for one- And two-dimensional magnetohydrodynamics equations. II; High-order semidiscrete schemes

SIAM Journal on Scientific Computing

Volumn 28, Issue 2, 2006, Pages 533-560

  Balbás, Jorge ^a   Tadmor, Eitan ^b  

^a UNIVERSITY OF MICHIGAN   (United States)

^b Bldg 142   (United States)

Author keywords

High resolution central schemes; Ideal magnetohydrodynamics (MHD) equations; Jacobian free form; Multidimensional conservation laws; Nonoscillatory reconstructions; Semi discrete schemes

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATION THEORY; MAGNETOHYDRODYNAMICS; PROBLEM SOLVING;

HIGH-RESOLUTION CENTRAL SCHEMES; IDEAL MAGNETOHYDRODYNAMICS (MHD) EQUATIONS; JACOBIAN-FREE FORM; MULTIDIMENSIONAL CONSERVATION LAWS; NONOSCILLATORY RECONSTRUCTIONS; SEMI-DISCRETE SCHEMES;

NONLINEAR EQUATIONS;

EID: 33847750208     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/040610246     Document Type: Article

References (28)

1. J. BALBÁS, Non-oscillatory Central Schemes for the Equations of Ideal Magnetohydrodynamics in One- and Two-Space Dimensions, Ph.D. thesis, University of California, Los Angeles, May 2004.
2. J. BALSÁS, E. TADMOR, AND C.-C. WU, Non-oscillatory central schemes for one- and twodimensional MHD equations. I, J. Comput. Phys., 201 (2004), pp. 261-285.
3. M. BRIO AND C. C. WU, An upwind differencing scheme for the equations of ideal magnetohydrodynamics, J. Comput. Phys., 75 (1988), pp. 400-422.
4. W. DAI AND P. R. WOODWARD, A simple finite difference scheme for multidimensional magnetohydrodynamical equations, J. Comput. Phys., 142 (1998), pp. 331- 369.
5. S. GOTTUEB, C.-W. SHU, AND E. TADMOR, Strong stability- preserving high-order time discretization methods, SIAM Rev., 43 (2001), pp. 89-112.
6. A. HARTEN, B. ENGQUIST, S. OSHER, AND S. R. CHAKRAVARTHY, Uniformly high-order accurate essentially nonoscillatory schemes. III, J. Comput. Phys., 71 (1987), pp. 231- 303.
7. A. HARTEN, High resolution schemes for hyperbolic conservation laws, J. Comput. Phys., 49 (1983), pp. 357-393.
8. G.-S. JIANG, D. LEVY, C.-T. LIN, S. OSHER, AND E. TADMOR, High-resolution nonoscillatory central schemes with nonstaggered grids for hyperbolic conservation laws, SIAM J. Numer. Anal., 35 (1998), pp. 2147-2168.
9. G.-S. JIANG AND C.-W. SHU, Efficient implementation of weighted ENO schemes, J. Comput. Phys., 126 (1996), pp. 202-228.
10. G.-S. JIANG AND E. TADMOR, Nonoscillatory central schemes for multidimensional hyperbolic conservation laws, SIAM J. Sci. Comput., 19 (1998), pp. 1892-1917.
11. G.-S. JIANG AND C.-C. WU, A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics, J. Comput. Phys., 150 (1999), pp. 561-594.
12. A. KURGANOV AND D. LEVY, A third-order semidiscrete central scheme for conservation laws and convection-diffusion equations, SIAM J. Sci. Comput., 22 (2000), pp. 1461-1488.
13. A. KURGANOV AND G. PETROVA, A third-order semi-discrete genuinely multidimensional central scheme for hyperbolic conservation laws and related problems, Numer. Math., 88 (2001), pp. 683-729.
14. A. KURGANOV AND E. TADMOR, New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations, J. Comput. Phys., 160 (2000), pp. 241-282.
15. P. D. LAX, Weak solutions of nonlinear hyperbolic equations and their numerical computation, Comm. Pure Appl. Math., 7 (1954), pp. 159-193.
16. D. LEVY, G. PUPPO, AND G. RUSSO, Central WENO schemes for hyperbolic systems of conservation laws, Math. Model. Numer. Anal., 33 (1999), pp. 547-571.
17. D. LEVY, G. PUPPO, AND G. RUSSO, A third order central WENO scheme for 2D conservation laws, Appl. Numer. Math., 33 (2000), pp. 415-421.
18. D. LEVY, G. PUPPO, AND G. RUSSO, A fourth-order central WENO scheme for multidimensional hyperbolic systems of conservation laws, SIAM J. Sci. Comput, 24 (2002), pp. 480-506 (electronic).
19. X.-D. LIU AND E. TADMOR, Third order nonoscillatory central scheme for hyperbolic conservation laws, Numer. Math., 79 (1998), pp. 397-425.
20. H. NESSYAHU AND E. TADMOR, Nonoscillatory central differencing for hyperbolic conservation laws, J. Comput. Phys., 87 (1990), pp. 408-463.
21. S. A. ORSZAG AND C. M. TANG, Small-scale structure of two- dimensional magnetohydrodynamic turbulence, J. Fluid Mech., 90 (1979), pp. 129-143.
22. K. G. POWELL, P. L. ROE, R. S MYONG, T. GOMBOSI, AND D. DE ZEEUW, An upwind scheme for magnetohydrodynamics, in Proceedings of the AIAA 12th Computational Fluid Dynamics Conference, San Diego, 1995, pp. 661-674.
23. C.-W. SHU, Total-variation-diminishing time discretizations, SIAM J. Sci. Statist. Comput., 9 (1988), pp. 1073-1084.
24. C.-W. SHU, Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, in Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, Lecture Notes in Math. 1697, Springer, Berlin, 1998, pp. 325-432.
25. C.-W. SHU AND S. OSHER, Efficient implementation of essentially nonoscillatory shockcapturing schemes. II, J. Comput. Phys., 83 (1989), pp. 32-78.
26. H.-Z. TANG AND K. XU, A high-order gas-kinetic method for multidimensional ideal magnetohydrodynamics, J. Comput. Phys., 165 (2000), pp. 69-88.
27. B. VAN LEER, Towards the ultimate conservative difference scheme. V. Second order sequel to Godunov method, J. Comput. Phys., 32 (1979), pp. 101-136.
28. C.-C. WU AND T. CHANG, Further study of the dynamics of two- dimensional MHD coherent structures-a large scale simulation, J. Atmospheric Solar-Terrestrial Phys., 95 (2001), pp. 1447-1453.