Solutions of the imploding shock problem in a medium with varying density

We consider the solutions of the Guderley problem, consisting of an imploding strong shock wave in an ideal gas with a power law initial density profile. The self-similar solutions, and, specifically, the similarity exponent that determines the behavior of the accelerating shock, are studied in deta...

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Bibliographic Details
Published inPhysics of fluids (1994) Vol. 33; no. 6
Main Authors Giron, Itamar, Balberg, Shmuel, Krief, Menahem
Format Journal Article
LanguageEnglish
Published Melville American Institute of Physics 01.06.2021
Subjects
Exact solutions
Fluid dynamics
Ideal gas
Physics
Self-similarity
Shock waves
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Summary:We consider the solutions of the Guderley problem, consisting of an imploding strong shock wave in an ideal gas with a power law initial density profile. The self-similar solutions, and, specifically, the similarity exponent that determines the behavior of the accelerating shock, are studied in detail, for cylindrical and spherical symmetries and for a wide range of the adiabatic index and the spatial density exponent. We then demonstrate how the analytic solutions can be reproduced in Lagrangian hydrodynamic codes, thus demonstrating their usefulness as a code validation and verification test problem.
ISSN:1070-6631
1089-7666
DOI:10.1063/5.0054525