A computational macroscale model for the time fractional poroelasticity problem in fractured and heterogeneous media
In this paper, we consider the poroelasticity problem with a time memory formalism that couples the pressure and displacement, and we assume this multiphysics process occurs in multicontinuum media. A coupled system of equations for pressures in each continuum and elasticity equations for displaceme...
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ir-20.500.12258-218602025-02-11T07:53:43Z A computational macroscale model for the time fractional poroelasticity problem in fractured and heterogeneous media Tyrylgin, A. A. Тырылгин, А. А. Alikhanov, A. A. Алиханов, А. А. Discrete fracture model Heterogeneous media Multicontinuum media Multiscale method Poroelasticity Time fractional derivative Fracture In this paper, we consider the poroelasticity problem with a time memory formalism that couples the pressure and displacement, and we assume this multiphysics process occurs in multicontinuum media. A coupled system of equations for pressures in each continuum and elasticity equations for displacements of the medium are included in the mathematical model. Based on the Caputo's time fractional derivative, we derive an implicit finite difference approximation for time discretization. Also, a Discrete Fracture Model (DFM) is used to model fluid flow through fractures and treat the complex network of fractures. Further, we develop a coarse grid approximation based on the Generalized Multiscale Finite Element Method (GMsFEM), where we solve local spectral problems for construction of the multiscale basis functions. The main idea of the proposed method is to reduce the dimensionality of the problem because our model equation has multiple fractional powers, there multiple unknowns with memory effects. Consequently, the solution is on a coarse grid, which saves some computational time. We present numerical results for the two-dimensional model problems in fractured heterogeneous porous media. After, we investigate error analysis between reference (fine-scale) solution and multiscale solution with different numbers of multiscale basis functions. The results show that on a coarse grid, the proposed approach can achieve good accuracy. 2022-11-21T08:28:05Z 2022-11-21T08:28:05Z 2022 Статья Tyrylgin, A., Vasilyeva, M., Alikhanov, A., Sheen, D. A computational macroscale model for the time fractional poroelasticity problem in fractured and heterogeneous media // Journal of Computational and Applied Mathematics. - 2022. - Том 418. - Номер статьи 114670. - DOI10.1016/j.cam.2022.114670 http://hdl.handle.net/20.500.12258/21860 en Journal of Computational and Applied Mathematics application/pdf application/pdf Elsevier B.V. |
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СКФУ |
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| language |
English |
| topic |
Discrete fracture model Heterogeneous media Multicontinuum media Multiscale method Poroelasticity Time fractional derivative Fracture |
| spellingShingle |
Discrete fracture model Heterogeneous media Multicontinuum media Multiscale method Poroelasticity Time fractional derivative Fracture Tyrylgin, A. A. Тырылгин, А. А. Alikhanov, A. A. Алиханов, А. А. A computational macroscale model for the time fractional poroelasticity problem in fractured and heterogeneous media |
| description |
In this paper, we consider the poroelasticity problem with a time memory formalism that couples the pressure and displacement, and we assume this multiphysics process occurs in multicontinuum media. A coupled system of equations for pressures in each continuum and elasticity equations for displacements of the medium are included in the mathematical model. Based on the Caputo's time fractional derivative, we derive an implicit finite difference approximation for time discretization. Also, a Discrete Fracture Model (DFM) is used to model fluid flow through fractures and treat the complex network of fractures. Further, we develop a coarse grid approximation based on the Generalized Multiscale Finite Element Method (GMsFEM), where we solve local spectral problems for construction of the multiscale basis functions. The main idea of the proposed method is to reduce the dimensionality of the problem because our model equation has multiple fractional powers, there multiple unknowns with memory effects. Consequently, the solution is on a coarse grid, which saves some computational time. We present numerical results for the two-dimensional model problems in fractured heterogeneous porous media. After, we investigate error analysis between reference (fine-scale) solution and multiscale solution with different numbers of multiscale basis functions. The results show that on a coarse grid, the proposed approach can achieve good accuracy. |
| format |
Статья |
| author |
Tyrylgin, A. A. Тырылгин, А. А. Alikhanov, A. A. Алиханов, А. А. |
| author_facet |
Tyrylgin, A. A. Тырылгин, А. А. Alikhanov, A. A. Алиханов, А. А. |
| author_sort |
Tyrylgin, A. A. |
| title |
A computational macroscale model for the time fractional poroelasticity problem in fractured and heterogeneous media |
| title_short |
A computational macroscale model for the time fractional poroelasticity problem in fractured and heterogeneous media |
| title_full |
A computational macroscale model for the time fractional poroelasticity problem in fractured and heterogeneous media |
| title_fullStr |
A computational macroscale model for the time fractional poroelasticity problem in fractured and heterogeneous media |
| title_full_unstemmed |
A computational macroscale model for the time fractional poroelasticity problem in fractured and heterogeneous media |
| title_sort |
computational macroscale model for the time fractional poroelasticity problem in fractured and heterogeneous media |
| publisher |
Elsevier B.V. |
| publishDate |
2022 |
| url |
https://dspace.ncfu.ru/handle/20.500.12258/21860 |
| work_keys_str_mv |
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