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A note on magnetic monopoles and the one-dimensional MHD Riemann problem. (English) Zbl 1065.35523


MSC:

35Q60 PDEs in connection with optics and electromagnetic theory
76W05 Magnetohydrodynamics and electrohydrodynamics
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References:

[1] Brackbill, J. U.; Barnes, D. C., The effect of nonzero ∇·B on the numerical solution of the magnetohydrodynamic equations, J. Comput. Phys., 35, 426 (1980) · Zbl 0429.76079
[2] Brio, M.; Wu, C. C., An upwind differencing scheme for the equations of ideal magnetohydrodynamics, J. Comput. Phys., 75, 400 (1988) · Zbl 0637.76125
[3] Godlewski, E.; Raviart, P.-A., Numerical Approximation of Hyperbolic Systems of Conservation Laws (1996) · Zbl 1063.65080
[4] Jackson, J. D., Classical Electrodynamics (1999) · Zbl 0114.42903
[5] Janhunen, P., A positive conservative method for magnetohydrodynamics based on HLL and Roe methods, J. Comput. Phys., 160, 649 (2000) · Zbl 0967.76061
[6] Landau, L. D.; Lifshitz, E. M., Fluid Mechanics (1987)
[7] R. J. LeVeque, Nonlinear conservation laws and finite volume methods for astrophysical fluid flow, in, Computational Methods for Astrophysical Fluid Flow, edited by, O. Steiner and A. Gautschy, 27th Saas-Fee Advanced Course Lecture Notes, Springer-Verlag, New York, 1998, p, 1.; R. J. LeVeque, Nonlinear conservation laws and finite volume methods for astrophysical fluid flow, in, Computational Methods for Astrophysical Fluid Flow, edited by, O. Steiner and A. Gautschy, 27th Saas-Fee Advanced Course Lecture Notes, Springer-Verlag, New York, 1998, p, 1.
[8] Misner, C. W.; Thorne, K. S.; Wheeler, J. A., Gravitation (1973)
[9] K. G. Powell, An Approximate Riemann Solver for Magnetohydrodynamics (That Works in More than One Dimension), ICASE Report No. 94-24, NASA Langley Research Center,1994);, available athttp://www.icase.edu/library/reports/rdp/1994.html#94-24; K. G. Powell, An Approximate Riemann Solver for Magnetohydrodynamics (That Works in More than One Dimension), ICASE Report No. 94-24, NASA Langley Research Center,1994);, available athttp://www.icase.edu/library/reports/rdp/1994.html#94-24
[10] Powell, K. G., Solution of the Euler and magnetohydrodynamic equations on solution-adaptive Cartesian grids, Computational Fluid Dynamics (1996)
[11] Powell, K. G.; Roe, P. L.; Linde, T. J.; Gombosi, T. I.; De Zeeuw, D. L., A solution-adaptive upwind scheme for ideal magnetohydrodynamics, J. Comput. Phys., 154, 284 (1999) · Zbl 0952.76045
[12] Rindler, W., Introduction to Special Relativity (1982) · Zbl 0507.70001
[13] Roe, P. L.; Balsara, D. S., Notes on the eigensystem of magnetohydrodynamics, SIAM J. Appl. Math., 56, 57 (1996) · Zbl 0845.35092
[14] Schwinger, J. S.; Deraad, L. L.; Milton, K. A.; Tsai, W.-Y., Classical Electrodynamics (1998)
[15] Tóth, G., The ∇middot;B=0 constraint in shock-capturing magnetohydrodynamics codes, J. Comput. Phys., 161, 605 (2000) · Zbl 0980.76051
[16] Woodward, P. R.; Dai, W., An approximate Riemann solver for ideal magnetohydrodynamics, J. Comput. Phys., 111, 354 (1994) · Zbl 0797.76052
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