Journal Article

A five-wave Harten–Lax–van Leer Riemann solver for relativistic magnetohydrodynamics

A. Mignone, M. Ugliano and G. Bodo

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 393, issue 4, pages 1141-1156
Published in print March 2009 | ISSN: 0035-8711
Published online February 2009 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2008.14221.x
A five-wave Harten–Lax–van Leer Riemann solver for relativistic magnetohydrodynamics

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We present a five-wave Riemann solver for the equations of ideal relativistic magneto-hydrodynamics. Our solver can be regarded as a relativistic extension of the five-wave HLLD Riemann solver initially developed by Miyoshi & Kusano for the equations of ideal magnetohydrodynamics. The solution to the Riemann problem is approximated by a five-wave pattern, comprising two outermost fast shocks, two rotational discontinuities and a contact surface in the middle. The proposed scheme is considerably more elaborate than in the classical case since the normal velocity is no longer constant across the rotational modes. Still, proper closure to the Rankine–Hugoniot jump conditions can be attained by solving a non-linear scalar equation in the total pressure variable which, for the chosen configuration, has to be constant over the whole Riemann fan. The accuracy of the new Riemann solver is validated against one-dimensional tests and multidimensional applications. It is shown that our new solver considerably improves over the popular Harten–Lax–van Leer solver or the recently proposed HLLC schemes.

Keywords: hydrodynamics; MHD; relativity; shock waves; methods: numerical

Journal Article.  9485 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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