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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2012, Volume 15, Number 3, Pages 271–280 (Mi sjvm479)  
This article is cited in 4 scientific papers (total in 4 papers)

On approximation of discontinuous solutions to the Buckley–Leverett equation

Yu. M. Laevsky, T. A. Kandryukova

Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Full-text PDF (575 kB) Citations (4)
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Abstract: In this paper, the Lax–Wendroff and “cabaret” schemes for the Buckley–Leverett equation are studied. It is shown that these schemes represent unstable solutions. The choice of an unstable solution depends on the Courant number, only. The finite element version of the “cabaret” scheme is given equation are studied. It is shown that these schemes represent unstable solutions. The choice of an unstable solution depends on the Courant number, only. The finite element version of the “cabaret” scheme is given.
Key words: Buckley–Leverett equation, Lax–Wendroff scheme, “cabaret” scheme, unstable solutions.
Received: 22.04.2011
Revised: 25.05.2011
English version:
Numerical Analysis and Applications, 2012, Volume 5, Issue 3, Pages 222–230
DOI: https://doi.org/10.1134/S1995423912030044
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
Citation: Yu. M. Laevsky, T. A. Kandryukova, “On approximation of discontinuous solutions to the Buckley–Leverett equation”, Sib. Zh. Vychisl. Mat., 15:3 (2012), 271–280; Num. Anal. Appl., 5:3 (2012), 222–230
Citation in format AMSBIB
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\by Yu.~M.~Laevsky, T.~A.~Kandryukova
\paper On approximation of discontinuous solutions to the Buckley--Leverett equation
\jour Sib. Zh. Vychisl. Mat.
\yr 2012
\vol 15
\issue 3
\pages 271--280
\mathnet{http://mi.mathnet.ru/sjvm479}
\elib{https://elibrary.ru/item.asp?id=20479424}
\transl
\jour Num. Anal. Appl.
\yr 2012
\vol 5
\issue 3
\pages 222--230
\crossref{https://doi.org/10.1134/S1995423912030044}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84865811366}
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    • This publication is cited in the following 4 articles:
    1. Alexander Sukhinov, Alexander Chistyakov, Inna Kuznetsova, Yulia Belova, Elena Rahimbaeva, “Development and Research of a Modified Upwind Leapfrog Scheme for Solving Transport Problems”, Mathematics, 10:19 (2022), 3564  crossref
    2. Ivanov M.I., Kremer I.A., Laevsky Yu.M., “On the Streamline Upwind Scheme of Solution to the Filtration Problem”, Sib. Electron. Math. Rep., 16 (2019), 757–776  mathnet  crossref  mathscinet  zmath  isi  scopus
    3. A. A. Cherevko, T. S. Gologush, I. A. Petrenko, V. V. Ostapenko, AIP Conference Proceedings, 2027, 2018, 040028  crossref
    4. K. Kovarik, S. Masarovicova, J. Muzik, D. Sitanyiova, “A meshless solution of two dimensional multiphase flow in porous media”, Eng. Anal. Bound. Elem., 70 (2016), 12–22  crossref  isi
    Citing articles in Google Scholar: Russian citations, English citations
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