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

Citation

Forbes, LK and Krzysik, OA, Shock-jump conditions in a general medium: weak-solution approach, Shock Waves, 27, (3) pp. 457-466. ISSN 0938-1287 (2017) [Refereed Article]

Copyright Statement

Copyright 2016 Springer-Verlag Berlin Heidelberg

DOI: doi:10.1007/s00193-016-0695-3

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 Details

Item Type:Refereed Article
Keywords:shock waves, jump conditions, weak solution, reactive flows, multi-dimensional shock, magnetohydrodynamic shock
Research Division:Mathematical Sciences
Research Group:Applied Mathematics
Research Field:Theoretical and Applied Mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Forbes, LK (Professor Larry Forbes)
Author:Krzysik, OA (Mr Oliver Krzysik)
ID Code:120312
Year Published:2017
Funding Support:Australian Research Council (DP140100094)
Deposited By:Mathematics and Physics
Deposited On:2017-08-21
Last Modified:2018-07-30
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