Geodesic
Mathematical modeling single-phase fluid flows in porous media
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 115-134

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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. 
@article{SEMR_2018_15_a111,
     author = {S. I. Markov and N. B. Itkina},
     title = {Mathematical modeling single-phase fluid flows in porous media},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {115--134},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a111/}
}
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S. I. Markov; N. B. Itkina. Mathematical modeling single-phase fluid flows in porous media. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 115-134. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a111/