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Matem. Mod., 2010, Volume 22, Number 4, Pages 118–128 (Mi mm2963)  

This article is cited in 4 scientific papers (total in 4 papers)

Explicit-implicit numerical algorithms for porous media multiphase flow problems

P. N. Vabishchevich

Institute for Mathematical Modeling RAS, Moscow, Russia

Abstract: The theoretical study on applied problems of oil and gas recovery is based on mathematical models for multiphase fluid flows in porous media. The basic model includes the continuity equation and the Darcy laws for each phase as well as the algebraic expression for the sum of saturations. A numerical algorithm is constructed using the pressure equation. In the present work there are discussed the basic conservation properties for the differential models and the necessity of their fulfillment at the discrete level. Explicit-implicit consistent approximations are constructed for multi-component flows in porous media along with the operator-splitting schemes for compressible media.

Keywords: multiphase flow, explicit-implicit algorithms, splitting scheme.

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English version:
Mathematical Models and Computer Simulations, 2010, 2:6, 682–690

Bibliographic databases:

UDC: 519.63+517.958
Received: 23.10.2008

Citation: P. N. Vabishchevich, “Explicit-implicit numerical algorithms for porous media multiphase flow problems”, Matem. Mod., 22:4 (2010), 118–128; Math. Models Comput. Simul., 2:6 (2010), 682–690

Citation in format AMSBIB
\Bibitem{Vab10}
\by P.~N.~Vabishchevich
\paper Explicit-implicit numerical algorithms for porous media multiphase flow problems
\jour Matem. Mod.
\yr 2010
\vol 22
\issue 4
\pages 118--128
\mathnet{http://mi.mathnet.ru/mm2963}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2731168}
\transl
\jour Math. Models Comput. Simul.
\yr 2010
\vol 2
\issue 6
\pages 682--690
\crossref{https://doi.org/10.1134/S2070048210060037}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84904898625}


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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. Afanaseva N.M., Vasileva M.V., Zakharov P.E., “Parallelnoe chislennoe modelirovanie protsessa zavodneniya neftyanogo mestorozhdeniya”, Matematicheskie zametki YaGU, 18:1 (2011), 159–172  mathscinet  zmath  elib
    2. E. B. Soboleva, “Metod chislennogo issledovaniya dinamiki solenoi vody v pochve”, Matem. modelirovanie, 26:2 (2014), 50–64  mathnet
    3. N. M. Afanas'eva, P. N. Vabishchevich, “Stable difference schemes for certain parabolic equations”, Comput. Math. Math. Phys., 54:7 (2014), 1159–1166  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. M. V. Vasileva, G. A. Prokopev, “Chislennoe reshenie zadachi dvukhfaznoi filtratsii s neodnorodnymi koeffitsientami metodom konechnykh elementov”, Matematicheskie zametki SVFU, 24:2 (2017), 46–62  mathnet  crossref  elib
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