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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2014, Volume 7, Issue 1, Pages 104–120 (Mi vyuru122)  

Mathematical Modelling

Shock Wave Structure in a Mixture of Condensed Media with Different Pressures

A. V. Fedorov

Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russian Federation

Abstract: We solve the problem of the structure of the shock wave in the heterogeneous mixture within the model of the mechanics of heterogeneous compressible media with different velocities, temperatures and pressures of components, using the laws of conservation of mass, momentum and energy for each phase, supplemented by kinetic equation compaction. Physical problem is reduced to the analysis of some boundary value problem for ordinary differential equation. The well-posedness of this problem was shown. This allows one to classify the types of shock waves in the mixture in the form of frozen and dispersive shock waves. Mathematical model is verified by experimental data on the shock adiabat mixture of aluminum and epoxy. The limiting conditions for the applicability of this model in describing the shock-wave experiments in a heterogeneous mixture of condensed materials are determined.

Keywords: mixture of compressible condensed media; relaxation shock wave; mathematical modeling.

DOI: https://doi.org/10.14529/mmp140109

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UDC: 533.6.011.72
MSC: 76T15
Received: 15.11.2013

Citation: A. V. Fedorov, “Shock Wave Structure in a Mixture of Condensed Media with Different Pressures”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 7:1 (2014), 104–120

Citation in format AMSBIB
\Bibitem{Fed14}
\by A.~V.~Fedorov
\paper Shock Wave Structure in a Mixture of Condensed Media with Different Pressures
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2014
\vol 7
\issue 1
\pages 104--120
\mathnet{http://mi.mathnet.ru/vyuru122}
\crossref{https://doi.org/10.14529/mmp140109}


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