Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 23
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Balsara, Dinshaw S. Montecinos, Gino I. and Toro, Eleuterio F. 2016. Exploring various flux vector splittings for the magnetohydrodynamic system. Journal of Computational Physics, Vol. 311, p. 1.

    Dumbser, Michael and Balsara, Dinshaw S. 2016. A new efficient formulation of the HLLEM Riemann solver for general conservative and non-conservative hyperbolic systems. Journal of Computational Physics, Vol. 304, p. 275.

    Lehmann, Andrew and Wardle, Mark 2016. Signatures of fast and slow magnetohydrodynamic shocks in turbulent molecular clouds. Monthly Notices of the Royal Astronomical Society, Vol. 455, Issue. 2, p. 2066.

    Dumbser, Michael 2014. Arbitrary-Lagrangian–Eulerian ADER–WENO finite volume schemes with time-accurate local time stepping for hyperbolic conservation laws. Computer Methods in Applied Mechanics and Engineering, Vol. 280, p. 57.

    McNally, Colin P. Maron, Jason L. and Mac Low, Mordecai-Mark 2012. PHURBAS: AN ADAPTIVE, LAGRANGIAN, MESHLESS, MAGNETOHYDRODYNAMICS CODE. II. IMPLEMENTATION AND TESTS. The Astrophysical Journal Supplement Series, Vol. 200, Issue. 1, p. 7.

    Van Loo, S Hartquist, T W and Falle, S A E G 2012. Magnetic fields and star formation. Astronomy & Geophysics, Vol. 53, Issue. 5, p. 5.31.

    DELMONT, P. and KEPPENS, R. 2011. Parameter regimes for slow, intermediate and fast MHD shocks. Journal of Plasma Physics, Vol. 77, Issue. 02, p. 207.

    Delmont, P and Keppens, R 2010. Regular shock refraction in planar ideal MHD. Journal of Physics: Conference Series, Vol. 216, p. 012007.

    Falle, Sam A.E.G. 2010. Encyclopedia of Aerospace Engineering.

    VAN LOO, S. FALLE, S. A. E. G. HARTQUIST, T. W. HAVNES, O. and MORFILL, G. E. 2010. Dusty magnetohydrodynamics in star-forming regions. Journal of Plasma Physics, Vol. 76, Issue. 3-4, p. 569.

    Wheatley, V. Kumar, H. and Huguenot, P. 2010. On the role of Riemann solvers in Discontinuous Galerkin methods for magnetohydrodynamics. Journal of Computational Physics, Vol. 229, Issue. 3, p. 660.

    Goedbloed, J. P. 2008. Time reversal duality of magnetohydrodynamic shocks. Physics of Plasmas, Vol. 15, Issue. 6, p. 062101.

    Giacomazzo, Bruno and Rezzolla, Luciano 2007. WhiskyMHD: a new numerical code for general relativistic magnetohydrodynamics. Classical and Quantum Gravity, Vol. 24, Issue. 12, p. S235.

    Ilin, K. I. and Trakhinin, Y. L. 2006. On the stability of Alfvén discontinuity. Physics of Plasmas, Vol. 13, Issue. 10, p. 102101.

    Lim, A. J. Falle, S. A. E. G. and Hartquist, T. W. 2005. The effect of dissipation on the generation of density structure by magnetohydrodynamic waves. Monthly Notices of the Royal Astronomical Society, Vol. 357, Issue. 2, p. 461.

    Andrianov, Nikolai and Warnecke, Gerald 2004. The Riemann problem for the Baer–Nunziato two-phase flow model. Journal of Computational Physics, Vol. 195, Issue. 2, p. 434.

    Ratkiewicz, Romana and Webb, Gary M. 2004. Reply to “Comment on “On the interaction of the solar wind with the interstellar medium: Field aligned MHD flow” by R. Ratkiewicz and G. M. Webb” by N. V. Pogorelov and T. Matsuda. Journal of Geophysical Research: Space Physics, Vol. 109, Issue. A2,

    Torrilhon, M. and Balsara, D.S. 2004. High order WENO schemes: investigations on non-uniform convergence for MHD Riemann problems. Journal of Computational Physics, Vol. 201, Issue. 2, p. 586.

    Warnecke, Gerald and Andrianov, Nikolai 2004. On the Solution to The Riemann Problem for the Compressible Duct Flow. SIAM Journal on Applied Mathematics, Vol. 64, Issue. 3, p. 878.

    Komissarov, S. S. 2003. Limit shocks of relativistic magnetohydrodynamics. Monthly Notices of the Royal Astronomical Society, Vol. 341, Issue. 2, p. 717.


On the inadmissibility of non-evolutionary shocks

  • S. A. E. G. FALLE (a1) and S. S. KOMISSAROV (a1)
  • DOI:
  • Published online: 01 July 2001

In recent years, numerical solutions of the equations of compressible magnetohydrodynamic (MHD) flows have been found to contain intermediate shocks for certain kinds of problems. Since these results would seem to be in conflict with the classical theory of MHD shocks, they have stimulated attempts to reexamine various aspects of this theory, in particular the role of dissipation. In this paper, we study the general relationship between the evolutionary conditions for discontinuous solutions of the dissipation-free system and the existence and uniqueness of steady dissipative shock structures for systems of quasilinear conservation laws with a concave entropy function. Our results confirm the classical theory. We also show that the appearance of intermediate shocks in numerical simulations can be understood in terms of the properties of the equations of planar MHD, for which some of these shocks turn out to be evolutionary. Finally, we discuss ways in which numerical schemes can be modified in order to avoid the appearance of intermediate shocks in simulations with such symmetry.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Plasma Physics
  • ISSN: 0022-3778
  • EISSN: 1469-7807
  • URL: /core/journals/journal-of-plasma-physics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *