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Shock waves and rarefaction waves in magnetohydrodynamics. Part 2. The MHD system

Published online by Cambridge University Press:  01 October 1997

R. S. MYONG  and
P. L. ROE
R. S. MYONG
Affiliation:
Present address: NASA Goddard Space Flight Center, Mail Stop 930, Greenbelt, Maryland 20771, USA. W. M. Keck Foundation Laboratory for Computational Fluid Dynamics, Department of Aerospace Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA
P. L. ROE
Affiliation:
W. M. Keck Foundation Laboratory for Computational Fluid Dynamics, Department of Aerospace Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA
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Abstract

In Part 1 of this study, a model set exactly preserving the MHD hyperbolic singularities was considered. By developing the viscosity admissibility condition, it was shown that the intermediate shocks are necessary to ensure that the planar Riemann problem is well-posed. Here in Part 2, the MHD Rankine–Hugoniot condition and rarefaction-wave relations are presented in phase space, which allows construction of analytical solutions of the planar MHD Riemann problem. In this process, a viscosity admissibility condition is proposed to determine physically admissible shocks. A complete account of MHD Hugoniot loci is given, leading to a classification of several subproblems in which the solution patterns are qualitatively same. Finally, it is shown that the planar MHD Riemann problem is well-posed using intermediate shocks that have been considered non-evolutionary.

Type
Research Article
Information
Journal of Plasma Physics , Volume 58 , Issue 3 , October 1997 , pp. 521 - 552
Copyright
1997 Cambridge University Press

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