Research reports

Years: 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

Exact Solver and Uniqueness Conditions for Riemann Problems of Ideal Magnetohydrodynamics

by M. Torrilhon

(Report number 2002-06)

Abstract
This paper presents the technical details necessary to implement an exact solver for the Riemann problem of magnetohydrodynamics (MHD) and investigates the uniqueness of MHD\Riemann solutions. The formulation of the solver results in a nonlinear algebraic 5 x 5 system of equations which has to be solved numerically. The equations of MHD form a non-strict hyperbolic system with non-convex fluxfunction. Thus special care is needed for possible non-regular waves, like compound waves or overcompressive shocks. The structure of the Hugoniot loci will be demonstrated and the non-regularity discussed. Several non-regular intermediate waves could be taken into account inside the solver. The non-strictness of the MHD system causes the Riemann problem also to be not unique. By virtue of the structure of the Hugoniot loci it follows, however, that the degree of freedom is reduced in the case of a non-regular solution. From this, uniqueness conditions for the Riemann problem of MHD are deduced.

Keywords: hyperbolic systems of conservation laws, Riemann problem, magnetohydrodynamics, non-classical shocks

@Techreport{T02_292,
  author = {M. Torrilhon},
  title = {Exact Solver and Uniqueness Conditions for Riemann Problems of Ideal Magnetohydrodynamics},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2002-06},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2002/2002-06.pdf },
  year = {2002}
}

Disclaimer
© Copyright for documents on this server remains with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use. The administrators respectfully request that authors inform them when any paper is published to avoid copyright infringement. Note that unauthorised copying of copyright material is illegal and may lead to prosecution. Neither the administrators nor the Seminar for Applied Mathematics (SAM) accept any liability in this respect. The most recent version of a SAM report may differ in formatting and style from published journal version. Do reference the published version if possible (see SAM Publications).