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Matematicheskoe modelirovanie, 2012, Volume 24, Number 5, Pages 112–130 (Mi mm3253)  
This article is cited in 1 scientific paper (total in 1 paper)

Mathematical models of a hydraulic shock in a slightly viscous liquid

A. M. Meirmanov, I. V. Nekrasova

Belgorod State University, Belgorod, Russia
Full-text PDF (360 kB) Citations (1)
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Abstract: In the present work are derive two mathematical models, describing the pressure distribution field in the layer near the borehole in process of the hydraulic fracturing. The derivation of the models is based on a rigorous homogenization of the exact mathematical model, governing on microscopic level the joint motion of an elastic solid skeleton and a viscous fluid filling the pores.
Keywords: hydraulic shock, Stokes and Lame's equations, two-scale convergence.
Received: 25.04.2011
English version:
Mathematical Models and Computer Simulations, 2012, Volume 4, Issue 6, Pages 597–610
DOI: https://doi.org/10.1134/S2070048212060087
Bibliographic databases:
Document Type: Article
UDC: 517.958:531.72, 517.958:539.3(4)
Language: Russian
Citation: A. M. Meirmanov, I. V. Nekrasova, “Mathematical models of a hydraulic shock in a slightly viscous liquid”, Mat. Model., 24:5 (2012), 112–130; Math. Models Comput. Simul., 4:6 (2012), 597–610
Citation in format AMSBIB
\Bibitem{MeiNek12}
\by A.~M.~Meirmanov, I.~V.~Nekrasova
\paper Mathematical models of a hydraulic shock in a slightly viscous liquid
\jour Mat. Model.
\yr 2012
\vol 24
\issue 5
\pages 112--130
\mathnet{http://mi.mathnet.ru/mm3253}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3025822}
\elib{https://elibrary.ru/item.asp?id=21276761}
\transl
\jour Math. Models Comput. Simul.
\yr 2012
\vol 4
\issue 6
\pages 597--610
\crossref{https://doi.org/10.1134/S2070048212060087}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84929089810}
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  • https://www.mathnet.ru/eng/mm3253
  • https://www.mathnet.ru/eng/mm/v24/i5/p112
    • This publication is cited in the following 1 articles:
    1. Peck D., Rogosin S.V., Wrobel M., Mishuris G., “Simulating the Hele-Shaw flow in the presence of various obstacles and moving particles”, Meccanica, 51:5 (2016), 1041–1055  crossref  mathscinet  zmath  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математическое моделирование
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    Abstract page:493
    Full-text PDF :172
    References:70
    First page:16
     
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