Online Meshfree Generalized Multiscale Finite Element Method for Flows in Fractured Media
Modeling fracture systems in porous media requires a specialized approach due to the high permeability of fractures, which significantly influences transport and flow processes. Fracture systems can exist at various scales and differ in their origins, complicating their modeling. This paper presents...
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2025
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ir-123456789-303602025-04-02T11:32:58Z Online Meshfree Generalized Multiscale Finite Element Method for Flows in Fractured Media Stepanov, S. P. Степанов, С. П. Discrete fractures Meshfree method Mathematical modeling Generalized multiscale finite element method Modeling fracture systems in porous media requires a specialized approach due to the high permeability of fractures, which significantly influences transport and flow processes. Fracture systems can exist at various scales and differ in their origins, complicating their modeling. This paper presents a generalized multiscale finite element method (GMsFEM) utilizing a meshfree approach for constructing the coarse grid. We develop a methodology for creating online multiscale basis functions computed during the solution of non-stationary problems, which account for changes in local subdomains. This approach reduces the number of offline basis functions required to achieve high accuracy. Comparative studies demonstrate the advantages of the online approach over traditional finite element methods on detailed grids. The online multiscale approach proves effective for problems in fractured porous media, albeit requiring additional computational resources. 2025-04-02T11:32:03Z 2025-04-02T11:32:03Z 2024 Статья Nikiforov D.Y., Stepanov S.P., Lazarev N.P. Online Meshfree Generalized Multiscale Finite Element Method for Flows in Fractured Media // Lobachevskii Journal of Mathematics. - 2024. - 45 (11). - pp. 5391 - 5401. - DOI: 10.1134/S1995080224606647 https://dspace.ncfu.ru/handle/123456789/30360 en Lobachevskii Journal of Mathematics application/pdf application/pdf Pleiades Publishing |
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Репозиторий |
| language |
English |
| topic |
Discrete fractures Meshfree method Mathematical modeling Generalized multiscale finite element method |
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Discrete fractures Meshfree method Mathematical modeling Generalized multiscale finite element method Stepanov, S. P. Степанов, С. П. Online Meshfree Generalized Multiscale Finite Element Method for Flows in Fractured Media |
| description |
Modeling fracture systems in porous media requires a specialized approach due to the high permeability of fractures, which significantly influences transport and flow processes. Fracture systems can exist at various scales and differ in their origins, complicating their modeling. This paper presents a generalized multiscale finite element method (GMsFEM) utilizing a meshfree approach for constructing the coarse grid. We develop a methodology for creating online multiscale basis functions computed during the solution of non-stationary problems, which account for changes in local subdomains. This approach reduces the number of offline basis functions required to achieve high accuracy. Comparative studies demonstrate the advantages of the online approach over traditional finite element methods on detailed grids. The online multiscale approach proves effective for problems in fractured porous media, albeit requiring additional computational resources. |
| format |
Статья |
| author |
Stepanov, S. P. Степанов, С. П. |
| author_facet |
Stepanov, S. P. Степанов, С. П. |
| author_sort |
Stepanov, S. P. |
| title |
Online Meshfree Generalized Multiscale Finite Element Method for Flows in Fractured Media |
| title_short |
Online Meshfree Generalized Multiscale Finite Element Method for Flows in Fractured Media |
| title_full |
Online Meshfree Generalized Multiscale Finite Element Method for Flows in Fractured Media |
| title_fullStr |
Online Meshfree Generalized Multiscale Finite Element Method for Flows in Fractured Media |
| title_full_unstemmed |
Online Meshfree Generalized Multiscale Finite Element Method for Flows in Fractured Media |
| title_sort |
online meshfree generalized multiscale finite element method for flows in fractured media |
| publisher |
Pleiades Publishing |
| publishDate |
2025 |
| url |
https://dspace.ncfu.ru/handle/123456789/30360 |
| work_keys_str_mv |
AT stepanovsp onlinemeshfreegeneralizedmultiscalefiniteelementmethodforflowsinfracturedmedia AT stepanovsp onlinemeshfreegeneralizedmultiscalefiniteelementmethodforflowsinfracturedmedia |
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