Falle, S.A.E.G. and Komissarov, S. (2001) On the inadmissibility of non-evolutionary shocks. Journal of Plasma Physics, 65 (1). pp. 29-58. ISSN 1469-7807Full text available as:
Available under licence : See the attached licence file.
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.
|Copyright, Publisher and Additional Information:||© 2001 Cambridge University Press|
|Institution:||The University of Leeds|
|Academic Units:||The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds)|
|Depositing User:||Repository Assistant|
|Date Deposited:||26 May 2006|
|Last Modified:||05 Jun 2014 08:56|
|Publisher:||Cambridge University Press|