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Matem. Mod., 2014, Volume 26, Number 9, Pages 111–125 (Mi mm3519)  

This article is cited in 2 scientific papers (total in 2 papers)

Numerical modeling of thermal stabilization of filter ground

P. N. Vabishchevicha, M. V. Vasilyevab, N. V. Pavlovab

a Nuclear Safety Institute, Russian Academy of Sciences, Moscow
b Ammosov North-Eastern Federal University, Yakutsk

Abstract: We consider the numerical simulation of the thermal stabilization (artificial freezing) filter soil around the base of the mine. Mathematical model based on the classical model of Stephen, which describes the process of heat transfer with phase change with the filter in a porous medium, and the system of equations for the temperature and pressure. Fictitious domain method is used for numerical solution of the resulting problem. Discretization of the system of equations is the finite element method, which is implemented in a software package FEniCSon high performance computing clusters. The numerical results are given and discussed.

Keywords: heat transfer, filtration, phase change, Stefan problem, fictitious domain method, finite element method, computing cluster.

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English version:
Mathematical Models and Computer Simulations, 2015, 7:2, 154–164

UDC: 519.63:517.958
Received: 18.04.2013

Citation: P. N. Vabishchevich, M. V. Vasilyeva, N. V. Pavlova, “Numerical modeling of thermal stabilization of filter ground”, Matem. Mod., 26:9 (2014), 111–125; Math. Models Comput. Simul., 7:2 (2015), 154–164

Citation in format AMSBIB
\Bibitem{VabVasPav14}
\by P.~N.~Vabishchevich, M.~V.~Vasilyeva, N.~V.~Pavlova
\paper Numerical modeling of thermal stabilization of filter ground
\jour Matem. Mod.
\yr 2014
\vol 26
\issue 9
\pages 111--125
\mathnet{http://mi.mathnet.ru/mm3519}
\transl
\jour Math. Models Comput. Simul.
\yr 2015
\vol 7
\issue 2
\pages 154--164
\crossref{https://doi.org/10.1134/S2070048215020106}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84929092828}


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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. P. N. Vabishchevich, S. P. Varlamov, V. I. Vasiliev, M. V. Vasilieva, S. P. Stepanov, “Numerical analysis of temperature dynamics of railway embankment in permafrost”, Math. Models Comput. Simul., 9:3 (2017), 292–304  mathnet  crossref  elib
    2. V. N. Alekseev, M. V. Vasileva, V. I. Vasilev, N. I. Sidnyaev, “Chislennoe modelirovanie svobodnoi konvektsii s uchetom fazovogo perekhoda”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 161, no. 3, Izd-vo Kazanskogo un-ta, Kazan, 2019, 327–340  mathnet  crossref
  • Математическое моделирование
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