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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.
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
Linking options:
https://www.mathnet.ru/eng/semr904 https://www.mathnet.ru/eng/semr/v15/p115
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Abstract page: | 233 | Full-text PDF : | 69 | References: | 32 |
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