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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2014, Volume 7, Issue 1, Pages 62–75 (Mi vyuru119)  

This article is cited in 1 scientific paper (total in 1 paper)

Mathematical Modelling

A Shock Capturing Method

V. F. Kuropatenko

Russian Federal Nuclear Center — Zababakhin Institute of Applied Physics, Snezhinsk, Russian Federation

Abstract: Strong discontinuities, or shocks in continua are a result of external dynamic loads. On the shock surface the conservation laws take the form of nonlinear algebraic equations for jumps across the shock. Entropy jumps across a strong discontinuity, and just this jump differs shocks from waves where the quantities vary continuously. In the heterogeneous difference schemes, the shock is treated as a layer of a finite thickness comparable with the cell size. This property of finite-difference schemes was called distraction. Since the state behind a shock is related to the state before it by the Hugoniot, in the distraction region there must act a mechanism that increases entropy. The physical viscosity and heat conductivity in continuum mechanics equations do not make it unnecessary to introduce a shock surface and hence cannot make the distraction length comparable with a few cells of the difference mesh. The paper considers a number of finite difference schemes where energy dissipation in the distraction region is defined by equations which are valid on the shock surface.

Keywords: shock wave; differential method; distraction; energy dissipation; conservation laws.

DOI: https://doi.org/10.14529/mmp140106

Full text: PDF file (330 kB)
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UDC: 519.63
MSC: 76.L, 74.S
Received: 15.12.2013

Citation: V. F. Kuropatenko, “A Shock Capturing Method”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 7:1 (2014), 62–75

Citation in format AMSBIB
\Bibitem{Kur14}
\by V.~F.~Kuropatenko
\paper A Shock Capturing Method
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2014
\vol 7
\issue 1
\pages 62--75
\mathnet{http://mi.mathnet.ru/vyuru119}
\crossref{https://doi.org/10.14529/mmp140106}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Krasilnikov, V. F. Kuropatenko, “Propagation of a strong discontinuity in a binary mixture of gases”, J. Comp. Eng. Math., 5:3 (2018), 49–60  mathnet  crossref  elib
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