V. I. Vasil'ev, M. V. Vasil'eva, V. S. Gladkikh, V. P. Ilin, D. Ya. Nikiforov, D. V. Perevozkin, G. A. Prokop'ev, “Numerical solution of a fluid filtration problem in a fractured medium by using the domain decomposition method”, Sib. Zh. Ind. Mat., 21:4 (2018), 15–27; J. Appl. Industr. Math., 12:4 (2018), 785

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Sibirskii Zhurnal Industrial'noi Matematiki, 2018, Volume 21, Number 4, Pages 15–27
DOI: https://doi.org/10.17377/sibjim.2018.21.402 (Mi sjim1018)

This article is cited in 11 scientific papers (total in 11 papers)

Numerical solution of a fluid filtration problem in a fractured medium by using the domain decomposition method

V. I. Vasil'ev^a, M. V. Vasil'eva^a, V. S. Gladkikh^b, V. P. Ilin^bc, D. Ya. Nikiforov^a, D. V. Perevozkin^b, G. A. Prokop'ev^a

^a Ammosov North-Eastern Federal University, ul. Belinskogo 58, Yakutsk, 677000 Russia
^b Institute of Computational Mathematics and Mathematical Geophysics, pr. Akad. Lavrent'eva 6, Novosibirsk, 630090 Russia
^c Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090 Russia

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DOI: https://doi.org/10.17377/sibjim.2018.21.402

Abstract: Under consideration are the numerical methods for simulation of a fluid flow in fractured porous media. The fractures are taken into account explicitly by using a discrete fracture model. The formulated single-phase filtering problem is approximated by an implicit finite element method on unstructured grids that resolve fractures at the grid level. The systems of linear algebraic equations (SLAE) are solved by the iterative methods of domain decomposition in the Krylov subspaces using the KRYLOV library of parallel algorithms. The results of solving some model problem are presented. A study is conducted of the efficiency of the computational implementation for various values of contrast coefficients which significantly affect the condition number and the number of iterations required for convergence of the method.

Keywords: filtering, fracturedmedium, discrete fracture model, approximation, flow rate, finite element method, unstructured grid, iterative method.

Funding agency	Grant number
Russian Foundation for Basic Research	16-29-15122 офи-м 18-01-00295 17-01-00732
Ministry of Education and Science of the Russian Federation	14.Y26.31.0013
The authors were supported by the Russian Foundation for Basic Research (projects nos. 16-29-15122_ofi_m, 18-01-00295, and 17-01-00732) and by the Megagrant of the Government of the Russian Federation (project no. 14.Y26.31.0013).

Received: 18.06.2018

English version:
Journal of Applied and Industrial Mathematics, 2018, Volume 12, Issue 4, Pages 785–796
DOI: https://doi.org/10.1134/S199047891804018X

Bibliographic databases:

Document Type: Article

UDC: 519.632.4

Language: Russian

Citation: V. I. Vasil'ev, M. V. Vasil'eva, V. S. Gladkikh, V. P. Ilin, D. Ya. Nikiforov, D. V. Perevozkin, G. A. Prokop'ev, “Numerical solution of a fluid filtration problem in a fractured medium by using the domain decomposition method”, Sib. Zh. Ind. Mat., 21:4 (2018), 15–27; J. Appl. Industr. Math., 12:4 (2018), 785–796

Citation in format AMSBIB

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Linking options:

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This publication is cited in the following 11 articles:

Denis Spiridonov, Maria Vasilyeva, “Non-local multi-continuum method (NLMC) for Darcy–Forchheimer flow in fractured media”, Journal of Computational and Applied Mathematics, 438 (2024), 115574
Djulustan Nikiforov, Sergei Stepanov, Nyurgun Lazarev, “Meshfree multiscale method for the infiltration problem in permafrost”, Journal of Computational and Applied Mathematics, 449 (2024), 115988
Djulustan Nikiforov, Sergei Stepanov, “Meshfree multiscale method with partially explicit time discretization for nonlinear Stefan problem”, Journal of Computational and Applied Mathematics, 451 (2024), 116020
D. Y. Nikiforov, S. P. Stepanov, N. P. Lazarev, “Online Meshfree Generalized Multiscale Finite Element Method for Flows in Fractured Media”, Lobachevskii J Math, 45:11 (2024), 5391
D. A. Spiridonov, J. Huang, “Multiscale Modeling with Online Correction for Darcy–Forchheimer Flow”, Lobachevskii J Math, 45:11 (2024), 5424
D. Y. Nikiforov, S. P. Stepanov, “Modeling of Artificial Ground Freezing Using a Meshfree Multiscale Method”, Lobachevskii J Math, 44:3 (2023), 1206
D. Y. Nikiforov, Y. Yang, “Meshfree Multiscale Method for Richards' Equation in Fractured Media”, Lobachevskii J Math, 44:10 (2023), 4135
Djulustan Nikiforov, “Meshfree Generalized Multiscale Finite Element Method”, Journal of Computational Physics, 474 (2023), 111798
V. I. Vasiliev, M. V. Vasilyeva, D. Ya. Nikiforov, N. I. Sidnyaev, S. P. Stepanov, A. N. Tseeva, “Computational implementation of a mixed-dimensional model of heat transfer in the soil–pipe system in cryolithic zone”, Comput. Math. Math. Phys., 61:12 (2021), 2054–2067
Petr V. Sivtsev, Djulustan Ya. Nikiforov, Lecture Notes in Computer Science, 11958, Large-Scale Scientific Computing, 2020, 365
Petr E. Zakharov, Petr V. Sivtsev, “Comparison of discrete fiber and asymptotic homogenization methods for modeling deformations of fiber-reinforced materials”, J. Phys.: Conf. Ser., 1392:1 (2019), 012078

Citing articles in Google Scholar: Russian citations, English citations
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Сибирский журнал индустриальной математики

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