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Shock-jump conditions in a general medium: weak-solution approach

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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 |
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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 |
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Item Statistics: | View statistics for this item |
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