Abstract:
The paper discusses a computational 3D double porosity model of a two-phase incompressible fluid filtration in a fractured-porous medium. Conservation laws are formulated in the integral form, and for their spatial approximation, a combination of the mixed finite element method to determine the total flow and pressure velocities is used and the finite volume method to determine the saturations in porous blocks and in fractures. The approximation of equations for saturations according to an explicit scheme with upwinding to eliminate unphysical oscillations is carried out. The model under consideration includes the injection and production wells with total flow rates. For the total velocities and pressures, the Neumann problem is formulated, for which the condition of unique solvability is indicated and a method for solving it without additional conditions is proposed. For an explicit upwind scheme for solving equations for saturations, a weak maximum principle is established, illustrated by computational experiments.
Citation:
M. I. Ivanov, I. A. Kremer, Yu. M. Laevsky, “A computational model of fluid filtration in fractured porous media”, Sib. Zh. Vychisl. Mat., 24:2 (2021), 145–166; Num. Anal. Appl., 14:2 (2021), 126–144
\Bibitem{IvaKreLae21}
\by M.~I.~Ivanov, I.~A.~Kremer, Yu.~M.~Laevsky
\paper A computational model of fluid filtration in fractured porous media
\jour Sib. Zh. Vychisl. Mat.
\yr 2021
\vol 24
\issue 2
\pages 145--166
\mathnet{http://mi.mathnet.ru/sjvm772}
\crossref{https://doi.org/10.15372/SJNM20210203}
\transl
\jour Num. Anal. Appl.
\yr 2021
\vol 14
\issue 2
\pages 126--144
\crossref{https://doi.org/10.1134/S1995423921020038}
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Linking options:
https://www.mathnet.ru/eng/sjvm772
https://www.mathnet.ru/eng/sjvm/v24/i2/p145
This publication is cited in the following 7 articles:
Maksim I. Ivanov, Igor A. Kremer, Yuri M. Laevsky, “Non-isothermal filtration problem: Two-temperature computational model”, Journal of Computational Physics, 531 (2025), 113941
Maksim I. Ivanov, Igor A. Kremer, Yuri M. Laevsky, “Explicit–implicit schemes for non-isothermal filtration problem: Single-temperature model”, Journal of Computational and Applied Mathematics, 440 (2024), 115639
Normakhmad Ravshanov, Iroda Kholmatova, Dilmurod Tukhtanazarov, INTERNATIONAL SCIENTIFIC CONFERENCE ON MODERN PROBLEMS OF APPLIED SCIENCE AND ENGINEERING: MPASE2024, 3244, INTERNATIONAL SCIENTIFIC CONFERENCE ON MODERN PROBLEMS OF APPLIED SCIENCE AND ENGINEERING: MPASE2024, 2024, 020004
Nozim Kurbonov, Shodmon Shokirov, Mumin Babajanov, INTERNATIONAL SCIENTIFIC CONFERENCE ON MODERN PROBLEMS OF APPLIED SCIENCE AND ENGINEERING: MPASE2024, 3244, INTERNATIONAL SCIENTIFIC CONFERENCE ON MODERN PROBLEMS OF APPLIED SCIENCE AND ENGINEERING: MPASE2024, 2024, 020052
Normakhmat Ravshanov, Iroda Kholmatova, Markhabo Shukurova, Asliddin Ne'matov, 2024 4th International Conference on Technological Advancements in Computational Sciences (ICTACS), 2024, 827
Maksim I. Ivanov, Igor A. Kremer, Yuri M. Laevsky, “On non-uniqueness of pressures in problems of fluid filtration in fractured-porous media”, Journal of Computational and Applied Mathematics, 425 (2023), 115052
M. I. Ivanov, I. A. Kremer, Yu. M. Laevsky, “Solving the Pure Neumann Problem by a Mixed Finite Element Method”, Numer. Analys. Appl., 15:4 (2022), 316
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