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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 115–134 (Mi semr904)  

Computational mathematics

Mathematical modeling single-phase fluid flows in porous media

S. I. Markovab, N. B. Itkinaa

a Novosibirsk State Technical University, Prospekt K. Marksa, 20, 630073, Novosibirsk, Russia
b Trofimuk Institute of Petroleum Geology and Geophysics SB RAS, Koptug ave. 3, 630090, Novosibirsk, Russia

Abstract: In the paper, we propose a modern mathematical method for solving seepage problems in multiscale porous media. We present a discrete variational formulation for a Discontinuous Galerkin Method (DG-method) with special stabilizing parameters. The DG-method is used for solving the single-phase fluid flow problem with full permeability tensor of the second rank in the macrolevel medium. A problem of homogenizing the heterogeneous mesolevel medium with non-periodic inclusions is considered. An algorithm for solving an inverse data problem is based on the Fletcher-Reeves method and the local Newton method. Mathematical modeling results of solving the seepage problem in the anisotropic heterogeneous and efficient media are given. A comparative analysis of the obtained mathematical modeling results is carried out.

Keywords: seepage problem, Discontinuous Galerkin Method, permeability tensor, homogenization.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation СП-3627.2016.5


DOI: https://doi.org/10.17377/semi.2018.15.013

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Bibliographic databases:

Document Type: Article
UDC: 519.633.2
MSC: 76S05
Received May 6, 2017, published February 12, 2018

Citation: S. I. Markov, N. B. Itkina, “Mathematical modeling single-phase fluid flows in porous media”, Sib. Èlektron. Mat. Izv., 15 (2018), 115–134

Citation in format AMSBIB
\Bibitem{MarItk18}
\by S.~I.~Markov, N.~B.~Itkina
\paper Mathematical modeling single-phase fluid flows in porous media
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 115--134
\mathnet{http://mi.mathnet.ru/semr904}
\crossref{https://doi.org/10.17377/semi.2018.15.013}


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