A Note on Magnetic Monopoles and the One Dimensional MHD Riemann Problem

This material has been published in Journal of Computational Physics, volume 172, September 2001, pages 329-398, the only definitive repository of the content that has been certified and accepted after peer review. Copyright © 2001 by Academic Press. Copyright and all rights therein are retained by Academic Press. This material may not be copied or reposted without explicit permission. This paper is available online from IDEAL (International Digital Electronic Access Library) at http://www.idealibrary.com.

Unfortunately, papers after 1999 from Academic Press are currently unavailable in Cambridge... so you may wish to read one of my online versions instead.

P. J. Dellar (2001) A Note on Magnetic Monopoles and the One Dimensional MHD Riemann Problem J. Comput. Phys. 172 pp. 392-398. DOI: 10.1006/jcph.2001.6815

Available as gzipped PostScript (Monopole.ps.gz 36K) or as PDF with hyperlinks (Monopole.pdf 106K). I believe they are both identical to the published paper apart from reformatting for A4 (or US letter) sized paper, and one misprint. The metric should be g=diag(-1,1,1,1) on page 394 just above equation (7), not G as printed.

Summary (Notes in J. Comput. Phys. are published without official abstracts)

This Note discusses extensions to the compressible magnetohydrodynamic (MHD) equations to accommodate magnetic monopoles, ie div B =/= 0, as may be expected to arise due to numerical truncation error. We show that a special relativistic formulation with an unmodified stress tensor leads to the equations recently proposed by Janhunen (2000) in the non-relativistic limit. These equation differ from those proposed by Powell (1994) in that they retain local conservation of energy and momentum in the presence of monopoles. Janhunen's equations also preserve positivity -- the solution of the Riemann problem will not contain unphysical intermediate states with negative pressures or densities.

P. Janhunen (2000) A positive conservative method for magnetohydrodynamics based on HLL and Roe methods J. Comput. Phys. 160 pp. 649-661. DOI: 10.1006/jcph.2000.6479

K. G. Powell (1994) An approximate Riemann solver for magnetohydrodynamics (that works in more than one dimension) ICASE Report No. 94-24

K. G. Powell et al. (1999) A solution-adaptive upwind scheme for ideal magnetohydrodynamics J. Comput. Phys. 154 pp. 284-309. DOI: 10.1006/jcph.1999.6299

BibTeX citation information:

@article{Dellar01Monopole,
author = "P. J. Dellar",
year = "2001",
title = "A Note on Magnetic Monopoles and the One Dimensional {MHD} {Riemann} Problem",
journal = "J. Comput. Phys.",
volume = "172",
pages = "392-398",
URL = "http://www.idealibrary.com/links/doi/10.1006/jcph.2001.6815",
DOI = "10.1006/jcph.2001.6815"}

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