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Shock-jump conditions in a general medium: weak-solution approach
journal contribution
posted on 2023-05-19, 10:03 authored by Lawrence ForbesLawrence Forbes, Krzysik, OAGeneral 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.
Funding
Australian Research Council
History
Publication title
Shock WavesVolume
27Pagination
457-466ISSN
0938-1287Department/School
School of Natural SciencesPublisher
Springer-VerlagPlace of publication
175 Fifth Ave, New York, USA, Ny, 10010Rights statement
Copyright 2016 Springer-Verlag Berlin HeidelbergRepository Status
- Restricted