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

Forbes, LK ORCID: 0000-0002-9135-3594 and Krzysik, OA 2017 , 'Shock-jump conditions in a general medium: weak-solution approach' , Shock Waves, vol. 27, no. 3 , pp. 457-466 , doi: 10.1007/s00193-016-0695-3.

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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

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