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Sib. Zh. Vychisl. Mat., 1998, Volume 1, Number 1, Pages 77–88 (Mi sjvm293)  

This article is cited in 3 scientific papers (total in 3 papers)

Approximation of Hugoniot's conditions by explicit conservative difference schemes for non-stationar shock waves

V. V. Ostapenko

M. A. Lavrent'ev Institute of Hydrodynamics, Novosibirsk

Abstract: Introducted here, is the concept of ($\varepsilon,\delta$)-Hugoniot's condition being the relatioship which links generalised solution magnitudes in points $(t-\delta,x(t)+\varepsilon)$ and $(t+\delta,x(t)-\varepsilon)$ for both sides of non-stationary shock wave front line $x=x(t)$. It is showed here, that the explicit bi-layer with respect to time conservative difference schemes for $\delta\ne0$ approximate ($\varepsilon,\delta$)-Hugoniot's conditions only with the first order, independent of their accuracy for smooth solutions. At the same time, if the front lines are quite smooth, then for $\delta=0$ these schemes approximate ($\varepsilon,0$)-Hugoniot's conditions with the same order they have for smooth solutions.

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Bibliographic databases:
UDC: 519.63
Received: 18.10.1997

Citation: V. V. Ostapenko, “Approximation of Hugoniot's conditions by explicit conservative difference schemes for non-stationar shock waves”, Sib. Zh. Vychisl. Mat., 1:1 (1998), 77–88

Citation in format AMSBIB
\Bibitem{Ost98}
\by V.~V.~Ostapenko
\paper Approximation of Hugoniot's conditions by explicit conservative difference schemes for non-stationar shock waves
\jour Sib. Zh. Vychisl. Mat.
\yr 1998
\vol 1
\issue 1
\pages 77--88
\mathnet{http://mi.mathnet.ru/sjvm293}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1699434}
\zmath{https://zbmath.org/?q=an:0906.76053}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. V. Ostapenko, “Raznostnaya skhema povyshennogo poryadka skhodimosti na nestatsionarnoi udarnoi volne”, Sib. zhurn. vychisl. matem., 2:1 (1999), 47–56  mathnet  zmath
    2. A. F. Voevodin, V. V. Ostapenko, “O raschete preryvnykh voln v otkrytykh ruslakh”, Sib. zhurn. vychisl. matem., 3:4 (2000), 305–321  mathnet  zmath
    3. V. V. Ostapenko, “Construction of high-order accurate shock-capturing finite difference schemes for unsteady shock waves”, Comput. Math. Math. Phys., 40:12 (2000), 1784–1800  mathnet  mathscinet  zmath  elib
  • Sibirskii Zhurnal Vychislitel'noi Matematiki
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