A full discretization of a time-dependent closed-loop geothermal system by a two-grid scheme
In this paper, a two-grid scheme for a time-dependent closed-loop geothermal system is proposed. The scheme solves a coupled partial differential equation model for this system on a coarse mesh with a mesh size of H and a decoupled problem on a fine mesh with a mesh size of h. In theoretical analysi...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2022-11-01
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| Series: | Results in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037422000668 |
| _version_ | 1811201856089620480 |
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| author | Xinyue Gao Yi Qin Jian Li Zhangxin Chen |
| author_facet | Xinyue Gao Yi Qin Jian Li Zhangxin Chen |
| author_sort | Xinyue Gao |
| collection | DOAJ |
| description | In this paper, a two-grid scheme for a time-dependent closed-loop geothermal system is proposed. The scheme solves a coupled partial differential equation model for this system on a coarse mesh with a mesh size of H and a decoupled problem on a fine mesh with a mesh size of h. In theoretical analysis, the stability and convergence of the two-grid scheme are proven. It is shown that when the coarse and fine mesh sizes satisfy h=H2, the accuracy of this scheme is almost the same as that of solving the nonlinear system directly on the fine mesh. At the same time, it saves a lot of calculation time and improves the efficiency of solving the coupled system. The effectiveness of the presented scheme is verified by numerical experiments. |
| first_indexed | 2024-04-12T02:28:58Z |
| format | Article |
| id | doaj.art-7bcb28812da645b9b89d46eb6ab262a8 |
| institution | Directory Open Access Journal |
| issn | 2590-0374 |
| language | English |
| last_indexed | 2024-04-12T02:28:58Z |
| publishDate | 2022-11-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Applied Mathematics |
| spelling | doaj.art-7bcb28812da645b9b89d46eb6ab262a82022-12-22T03:51:53ZengElsevierResults in Applied Mathematics2590-03742022-11-0116100343A full discretization of a time-dependent closed-loop geothermal system by a two-grid schemeXinyue Gao0Yi Qin1Jian Li2Zhangxin Chen3School of Mathematics and Data Science, Shaanxi University of science and technology, Xi’an, Shaanxi 710016, ChinaSchool of Mathematics and Data Science, Shaanxi University of science and technology, Xi’an, Shaanxi 710016, ChinaSchool of Mathematics and Data Science, Shaanxi University of science and technology, Xi’an, Shaanxi 710016, China; Corresponding author.Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, AB T2N 1N4, CanadaIn this paper, a two-grid scheme for a time-dependent closed-loop geothermal system is proposed. The scheme solves a coupled partial differential equation model for this system on a coarse mesh with a mesh size of H and a decoupled problem on a fine mesh with a mesh size of h. In theoretical analysis, the stability and convergence of the two-grid scheme are proven. It is shown that when the coarse and fine mesh sizes satisfy h=H2, the accuracy of this scheme is almost the same as that of solving the nonlinear system directly on the fine mesh. At the same time, it saves a lot of calculation time and improves the efficiency of solving the coupled system. The effectiveness of the presented scheme is verified by numerical experiments.http://www.sciencedirect.com/science/article/pii/S2590037422000668Closed-loop geothermal systemTwo-grid schemeDecoupled method |
| spellingShingle | Xinyue Gao Yi Qin Jian Li Zhangxin Chen A full discretization of a time-dependent closed-loop geothermal system by a two-grid scheme Results in Applied Mathematics Closed-loop geothermal system Two-grid scheme Decoupled method |
| title | A full discretization of a time-dependent closed-loop geothermal system by a two-grid scheme |
| title_full | A full discretization of a time-dependent closed-loop geothermal system by a two-grid scheme |
| title_fullStr | A full discretization of a time-dependent closed-loop geothermal system by a two-grid scheme |
| title_full_unstemmed | A full discretization of a time-dependent closed-loop geothermal system by a two-grid scheme |
| title_short | A full discretization of a time-dependent closed-loop geothermal system by a two-grid scheme |
| title_sort | full discretization of a time dependent closed loop geothermal system by a two grid scheme |
| topic | Closed-loop geothermal system Two-grid scheme Decoupled method |
| url | http://www.sciencedirect.com/science/article/pii/S2590037422000668 |
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