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Abstract

General conservation laws are considered, and the concept of a weak solution is extended to the case of an equation involving three space variables and time. Four-dimensional vector calculus is used to develop general jump conditions at a shock wave in the material. To illustrate the use of this result, jump conditions at a shock in unsteady three-dimensional compressible gas flow are presented. It is then proved rigorously that these reduce to the commonly assumed conditions in coordinates normal and tangential to the shock face. A similar calculation is also outlined for an unsteady three-dimensional shock in magnetohydrodynamics, and in a chemically reactive fluid. The technique is available for determining shock–jump conditions in quite general continuous media.

Item Type:	Article
Authors/Creators:	Forbes, LK and Krzysik, OA
Keywords:	shock waves, jump conditions, weak solution, reactive flows, multi-dimensional shock, magnetohydrodynamic shock
Journal or Publication Title:	Shock Waves
Publisher:	Springer-Verlag
ISSN:	0938-1287
DOI / ID Number:	10.1007/s00193-016-0695-3
Copyright Information:	Copyright 2016 Springer-Verlag Berlin Heidelberg
Related URLs:	Google Scholar: Forbes, LK UTAS Profile: Forbes, LK
Item Statistics:	View statistics for this item

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