Mixed Generalized Multiscale Finite Element Method for a Simplified Magnetohydrodynamics Problem in Perforated Domains
In this paper, we consider a coupled system of equations that describes simplified magnetohydrodynamics (MHD) problem in perforated domains. We construct a fine grid that resolves the perforations on the grid level in order to use a traditional approximation. For the solution on the fine grid, we co...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-06-01
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| Series: | Computation |
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| Online Access: | https://www.mdpi.com/2079-3197/8/2/58 |
| _version_ | 1797564473450430464 |
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| author | Valentin Alekseev Qili Tang Maria Vasilyeva Eric T. Chung Yalchin Efendiev |
| author_facet | Valentin Alekseev Qili Tang Maria Vasilyeva Eric T. Chung Yalchin Efendiev |
| author_sort | Valentin Alekseev |
| collection | DOAJ |
| description | In this paper, we consider a coupled system of equations that describes simplified magnetohydrodynamics (MHD) problem in perforated domains. We construct a fine grid that resolves the perforations on the grid level in order to use a traditional approximation. For the solution on the fine grid, we construct approximation using the mixed finite element method. To reduce the size of the fine grid system, we will develop a Mixed Generalized Multiscale Finite Element Method (Mixed GMsFEM). The method differs from existing approaches and requires some modifications to represent the flow and magnetic fields. Numerical results are presented for a two-dimensional model problem in perforated domains. This model problem is a special case for the general 3D problem. We study the influence of the number of multiscale basis functions on the accuracy of the method and show that the proposed method provides a good accuracy with few basis functions. |
| first_indexed | 2024-03-10T18:57:45Z |
| format | Article |
| id | doaj.art-df79c411cbc84f29bf7a39e63393130c |
| institution | Directory Open Access Journal |
| issn | 2079-3197 |
| language | English |
| last_indexed | 2024-03-10T18:57:45Z |
| publishDate | 2020-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computation |
| spelling | doaj.art-df79c411cbc84f29bf7a39e63393130c2023-11-20T04:39:51ZengMDPI AGComputation2079-31972020-06-01825810.3390/computation8020058Mixed Generalized Multiscale Finite Element Method for a Simplified Magnetohydrodynamics Problem in Perforated DomainsValentin Alekseev0Qili Tang1Maria Vasilyeva2Eric T. Chung3Yalchin Efendiev4Multiscale Model Reduction Laboratory, North-Eastern Federal University, 677007 Yakutsk, RussiaHunan Key Laboratory for Computation and Simulation in Science and Engineering, Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, ChinaMultiscale Model Reduction Laboratory, North-Eastern Federal University, 677007 Yakutsk, RussiaDepartment of Mathematics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong 999077, ChinaDepartment of Mathematics, Texas A&M University, College Station, TX 77843, USAIn this paper, we consider a coupled system of equations that describes simplified magnetohydrodynamics (MHD) problem in perforated domains. We construct a fine grid that resolves the perforations on the grid level in order to use a traditional approximation. For the solution on the fine grid, we construct approximation using the mixed finite element method. To reduce the size of the fine grid system, we will develop a Mixed Generalized Multiscale Finite Element Method (Mixed GMsFEM). The method differs from existing approaches and requires some modifications to represent the flow and magnetic fields. Numerical results are presented for a two-dimensional model problem in perforated domains. This model problem is a special case for the general 3D problem. We study the influence of the number of multiscale basis functions on the accuracy of the method and show that the proposed method provides a good accuracy with few basis functions.https://www.mdpi.com/2079-3197/8/2/58generalized multiscale finite element methodmagnetohydrodynamicsperforated domain |
| spellingShingle | Valentin Alekseev Qili Tang Maria Vasilyeva Eric T. Chung Yalchin Efendiev Mixed Generalized Multiscale Finite Element Method for a Simplified Magnetohydrodynamics Problem in Perforated Domains Computation generalized multiscale finite element method magnetohydrodynamics perforated domain |
| title | Mixed Generalized Multiscale Finite Element Method for a Simplified Magnetohydrodynamics Problem in Perforated Domains |
| title_full | Mixed Generalized Multiscale Finite Element Method for a Simplified Magnetohydrodynamics Problem in Perforated Domains |
| title_fullStr | Mixed Generalized Multiscale Finite Element Method for a Simplified Magnetohydrodynamics Problem in Perforated Domains |
| title_full_unstemmed | Mixed Generalized Multiscale Finite Element Method for a Simplified Magnetohydrodynamics Problem in Perforated Domains |
| title_short | Mixed Generalized Multiscale Finite Element Method for a Simplified Magnetohydrodynamics Problem in Perforated Domains |
| title_sort | mixed generalized multiscale finite element method for a simplified magnetohydrodynamics problem in perforated domains |
| topic | generalized multiscale finite element method magnetohydrodynamics perforated domain |
| url | https://www.mdpi.com/2079-3197/8/2/58 |
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