A Modular Grad-Div Stabilization Method for Time-Dependent Thermally Coupled MHD Equations
In this paper, we consider a fully discrete modular grad-div stabilization algorithm for time-dependent thermally coupled magnetohydrodynamic (MHD) equations. The main idea of the proposed algorithm is to add an extra minimally intrusive module to penalize the divergence errors of velocity and impro...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/24/10/1336 |
| _version_ | 1797473533042884608 |
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| author | Xianzhu Li Haiyan Su |
| author_facet | Xianzhu Li Haiyan Su |
| author_sort | Xianzhu Li |
| collection | DOAJ |
| description | In this paper, we consider a fully discrete modular grad-div stabilization algorithm for time-dependent thermally coupled magnetohydrodynamic (MHD) equations. The main idea of the proposed algorithm is to add an extra minimally intrusive module to penalize the divergence errors of velocity and improve the computational efficiency for increasing values of the Reynolds number and grad-div stabilization parameters. In addition, we provide the unconditional stability and optimal convergence analysis of this algorithm. Finally, several numerical experiments are performed and further indicated these advantages over the algorithm without grad-div stabilization. |
| first_indexed | 2024-03-09T20:15:50Z |
| format | Article |
| id | doaj.art-ba88aa4f1f6f49c399c049116fc04e69 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T20:15:50Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-ba88aa4f1f6f49c399c049116fc04e692023-11-24T00:01:56ZengMDPI AGEntropy1099-43002022-09-012410133610.3390/e24101336A Modular Grad-Div Stabilization Method for Time-Dependent Thermally Coupled MHD EquationsXianzhu Li0Haiyan Su1College of Mathematics and System Science, Xinjiang University, Urumqi 830017, ChinaCollege of Mathematics and System Science, Xinjiang University, Urumqi 830017, ChinaIn this paper, we consider a fully discrete modular grad-div stabilization algorithm for time-dependent thermally coupled magnetohydrodynamic (MHD) equations. The main idea of the proposed algorithm is to add an extra minimally intrusive module to penalize the divergence errors of velocity and improve the computational efficiency for increasing values of the Reynolds number and grad-div stabilization parameters. In addition, we provide the unconditional stability and optimal convergence analysis of this algorithm. Finally, several numerical experiments are performed and further indicated these advantages over the algorithm without grad-div stabilization.https://www.mdpi.com/1099-4300/24/10/1336thermally coupled MHDmodular grad-div stabilizationstabilityoptimal convergence |
| spellingShingle | Xianzhu Li Haiyan Su A Modular Grad-Div Stabilization Method for Time-Dependent Thermally Coupled MHD Equations Entropy thermally coupled MHD modular grad-div stabilization stability optimal convergence |
| title | A Modular Grad-Div Stabilization Method for Time-Dependent Thermally Coupled MHD Equations |
| title_full | A Modular Grad-Div Stabilization Method for Time-Dependent Thermally Coupled MHD Equations |
| title_fullStr | A Modular Grad-Div Stabilization Method for Time-Dependent Thermally Coupled MHD Equations |
| title_full_unstemmed | A Modular Grad-Div Stabilization Method for Time-Dependent Thermally Coupled MHD Equations |
| title_short | A Modular Grad-Div Stabilization Method for Time-Dependent Thermally Coupled MHD Equations |
| title_sort | modular grad div stabilization method for time dependent thermally coupled mhd equations |
| topic | thermally coupled MHD modular grad-div stabilization stability optimal convergence |
| url | https://www.mdpi.com/1099-4300/24/10/1336 |
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