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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2016, Volume 9, Issue 1, Pages 5–19 (Mi vyuru298)  

Mathematical Modelling

Shock waves in gas sphere

V. F. Kuropatenkoab, E. S. Shestakovskayab, M. N. Yakimovaa

a Russian Federal Nuclear Center — Zababakhin All-Russia Research Institute of Technical Physics, Snezhinsk, Russian Federation
b South Ural State University, Chelyabinsk, Russian Federation

Abstract: Mathematical modelling is widely applied for researches in all natural sciences, industries, economy, biology and other areas. Already existing or new created models and numerical methods are used for the solution of specific problems. The most reliable way to check the adequacy of the differential scheme is to compare the numerical solution with the precise solution of the problem where it is possible. As an example of such "reference" solution we construct a precise solution for the problem of a convergent shock wave and dynamic gas compression in a spherical vessel with an impermeable wall. Initially, the external border of the gas begins to move stepwise with a negative velocity, and the shock wave begins to propagate from border to gas. Acceleration of the border and sphericity determine the motion of the shock wave and the structure of the gas flow between the shock front and border. The considered problem formulation is fundamentally different from previously known statements of the problem of self-similar shock wave convergence to the center of symmetry and its reflection from the center with no boundary of gas.

Keywords: shock wave; analytical solution; ideal gas; spherical symmetry.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00072_


DOI: https://doi.org/10.14529/mmp160101

Full text: PDF file (701 kB)
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Bibliographic databases:

UDC: 533.6.011.1
MSC: 76N15
Received: 30.11.2015

Citation: V. F. Kuropatenko, E. S. Shestakovskaya, M. N. Yakimova, “Shock waves in gas sphere”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 9:1 (2016), 5–19

Citation in format AMSBIB
\Bibitem{KurSheYak16}
\by V.~F.~Kuropatenko, E.~S.~Shestakovskaya, M.~N.~Yakimova
\paper Shock waves in gas sphere
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2016
\vol 9
\issue 1
\pages 5--19
\mathnet{http://mi.mathnet.ru/vyuru298}
\crossref{https://doi.org/10.14529/mmp160101}
\elib{http://elibrary.ru/item.asp?id=25717229}


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