Partial learning using partially explicit discretization for multicontinuum/multiscale problems. Fractured poroelastic media simulation

The poroelasticity problem plays a vital role in various fields of science and technology. For example, it has applications in the petroleum industry, agricultural science, and biomedicine. The mathematical model consists of a coupled system of differential equations for mechanical displacements and...

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Κύριοι συγγραφείς:	Tyrylgin, A. A., Тырылгин, А. А.
Μορφή:	Статья
Γλώσσα:	English
Έκδοση:	2023
Θέματα:	Fractured poroelastic media simulation Partial learning Discretizations Multicontinuum problems Multiscale problems
Διαθέσιμο Online:	https://dspace.ncfu.ru/handle/20.500.12258/23475
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record_format	dspace
spelling	ir-20.500.12258-234752023-05-12T12:43:09Z Partial learning using partially explicit discretization for multicontinuum/multiscale problems. Fractured poroelastic media simulation Tyrylgin, A. A. Тырылгин, А. А. Fractured poroelastic media simulation Partial learning Discretizations Multicontinuum problems Multiscale problems The poroelasticity problem plays a vital role in various fields of science and technology. For example, it has applications in the petroleum industry, agricultural science, and biomedicine. The mathematical model consists of a coupled system of differential equations for mechanical displacements and pressure. In this paper, we propose a new approach for solving the poroelasticity problem in a fractured medium based on hybrid explicit–implicit learning (HEI). For spatial approximation, we use the finite element method with standard linear basis functions. We consider a poroelastic medium with large hydraulic fractures and use the Discrete Fracture Model. For the time approximation, we apply the explicit–implicit scheme. The explicit scheme is used for the porous matrix, which is a low-conductive continuum. While for fractures, we apply the implicit scheme due to its high conductivity. To facilitate the calculations, we use the fixed strain and fixed stress splitting schemes. The main idea of the proposed method lies in partial learning. Full training of the numerical solution is extremely difficult due to a large number of degrees of freedom, so we propose to train a part of the solution. Large hydraulic fractures have few degrees of freedom, but they are highly conductive and require a more costly implicit scheme. Therefore, we train the neural network to generate pressure in the fractures at several time points and then interpolate for other times. Thus, we treat the fracture pressure as a known function and use it to find the pressure in the porous matrix. Numerical results for a two-dimensional model problem are presented. 2023-05-12T12:30:20Z 2023-05-12T12:30:20Z 2023 Статья Ammosov, D., Grigorev, A., Stepanov, S., Tyrylgin, A. Partial learning using partially explicit discretization for multicontinuum/multiscale problems. Fractured poroelastic media simulation // Journal of Computational and Applied Mathematics. - 2023. - 424, № 115003. - DOI: 10.1016/j.cam.2022.115003 http://hdl.handle.net/20.500.12258/23475 en Journal of Computational and Applied Mathematics application/pdf application/pdf
institution	СКФУ
collection	Репозиторий
language	English
topic	Fractured poroelastic media simulation Partial learning Discretizations Multicontinuum problems Multiscale problems
spellingShingle	Fractured poroelastic media simulation Partial learning Discretizations Multicontinuum problems Multiscale problems Tyrylgin, A. A. Тырылгин, А. А. Partial learning using partially explicit discretization for multicontinuum/multiscale problems. Fractured poroelastic media simulation
description	The poroelasticity problem plays a vital role in various fields of science and technology. For example, it has applications in the petroleum industry, agricultural science, and biomedicine. The mathematical model consists of a coupled system of differential equations for mechanical displacements and pressure. In this paper, we propose a new approach for solving the poroelasticity problem in a fractured medium based on hybrid explicit–implicit learning (HEI). For spatial approximation, we use the finite element method with standard linear basis functions. We consider a poroelastic medium with large hydraulic fractures and use the Discrete Fracture Model. For the time approximation, we apply the explicit–implicit scheme. The explicit scheme is used for the porous matrix, which is a low-conductive continuum. While for fractures, we apply the implicit scheme due to its high conductivity. To facilitate the calculations, we use the fixed strain and fixed stress splitting schemes. The main idea of the proposed method lies in partial learning. Full training of the numerical solution is extremely difficult due to a large number of degrees of freedom, so we propose to train a part of the solution. Large hydraulic fractures have few degrees of freedom, but they are highly conductive and require a more costly implicit scheme. Therefore, we train the neural network to generate pressure in the fractures at several time points and then interpolate for other times. Thus, we treat the fracture pressure as a known function and use it to find the pressure in the porous matrix. Numerical results for a two-dimensional model problem are presented.
format	Статья
author	Tyrylgin, A. A. Тырылгин, А. А.
author_facet	Tyrylgin, A. A. Тырылгин, А. А.
author_sort	Tyrylgin, A. A.
title	Partial learning using partially explicit discretization for multicontinuum/multiscale problems. Fractured poroelastic media simulation
title_short	Partial learning using partially explicit discretization for multicontinuum/multiscale problems. Fractured poroelastic media simulation
title_full	Partial learning using partially explicit discretization for multicontinuum/multiscale problems. Fractured poroelastic media simulation
title_fullStr	Partial learning using partially explicit discretization for multicontinuum/multiscale problems. Fractured poroelastic media simulation
title_full_unstemmed	Partial learning using partially explicit discretization for multicontinuum/multiscale problems. Fractured poroelastic media simulation
title_sort	partial learning using partially explicit discretization for multicontinuum/multiscale problems. fractured poroelastic media simulation
publishDate	2023
url	https://dspace.ncfu.ru/handle/20.500.12258/23475
work_keys_str_mv	AT tyrylginaa partiallearningusingpartiallyexplicitdiscretizationformulticontinuummultiscaleproblemsfracturedporoelasticmediasimulation AT tyrylginaa partiallearningusingpartiallyexplicitdiscretizationformulticontinuummultiscaleproblemsfracturedporoelasticmediasimulation
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Partial learning using partially explicit discretization for multicontinuum/multiscale problems. Fractured poroelastic media simulation

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