Geodesic
Calculation of outgoing shock waves in the empty cavity collapse problem
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 1, pp. 44-54

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The self-similar problem about a collapse of an empty cylindrical or spherical cavity in compressible fluid with adiabatic exponent $\gamma$ is considered. Two possible variants of the flow after collapse are discussed. The variants are connected with the entropy behavior through the outgoing shock. The calculations show that the main difference in the flow quantities behavior at reflection stage have a quantitative character. Outgoing shock compression ratio, characterized by relation $\rho_2/\rho_1$, decreases for both variants of the reflection when $\gamma$ is increase. 
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     author = {V. S. Kozhanov},
     title = {Calculation of outgoing shock waves in the empty cavity collapse problem},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {44--54},
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     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2010_10_1_a7/}
}
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V. S. Kozhanov. Calculation of outgoing shock waves in the empty cavity collapse problem. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 1, pp. 44-54. http://geodesic.mathdoc.fr/item/ISU_2010_10_1_a7/