Linear Full Decoupling, Velocity Correction Method for Unsteady Thermally Coupled Incompressible Magneto-Hydrodynamic Equations
We propose and analyze an effective decoupling algorithm for unsteady thermally coupled magneto-hydrodynamic equations in this paper. The proposed method is a first-order velocity correction projection algorithms in time marching, including standard velocity correction and rotation velocity correcti...
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| Format: | Article |
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MDPI AG
2022-08-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/24/8/1159 |
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| author | Zhe Zhang Haiyan Su Xinlong Feng |
| author_facet | Zhe Zhang Haiyan Su Xinlong Feng |
| author_sort | Zhe Zhang |
| collection | DOAJ |
| description | We propose and analyze an effective decoupling algorithm for unsteady thermally coupled magneto-hydrodynamic equations in this paper. The proposed method is a first-order velocity correction projection algorithms in time marching, including standard velocity correction and rotation velocity correction, which can completely decouple all variables in the model. Meanwhile, the schemes are not only linear and only need to solve a series of linear partial differential equations with constant coefficients at each time step, but also the standard velocity correction algorithm can produce the Neumann boundary condition for the pressure field, but the rotational velocity correction algorithm can produce the consistent boundary which improve the accuracy of the pressure field. Thus, improving our computational efficiency. Then, we give the energy stability of the algorithms and give a detailed proofs. The key idea to establish the stability results of the rotation velocity correction algorithm is to transform the rotation term into a telescopic symmetric form by means of the Gauge–Uzawa formula. Finally, numerical experiments show that the rotation velocity correction projection algorithm is efficient to solve the thermally coupled magneto-hydrodynamic equations. |
| first_indexed | 2024-03-09T09:57:40Z |
| format | Article |
| id | doaj.art-b630beb9fdd8429a9816cf65ba89f2b4 |
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| language | English |
| last_indexed | 2024-03-09T09:57:40Z |
| publishDate | 2022-08-01 |
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| spelling | doaj.art-b630beb9fdd8429a9816cf65ba89f2b42023-12-01T23:40:31ZengMDPI AGEntropy1099-43002022-08-01248115910.3390/e24081159Linear Full Decoupling, Velocity Correction Method for Unsteady Thermally Coupled Incompressible Magneto-Hydrodynamic EquationsZhe Zhang0Haiyan Su1Xinlong Feng2College of Mathematics and System Science, Xinjiang University, Urumqi 830046, ChinaCollege of Mathematics and System Science, Xinjiang University, Urumqi 830046, ChinaCollege of Mathematics and System Science, Xinjiang University, Urumqi 830046, ChinaWe propose and analyze an effective decoupling algorithm for unsteady thermally coupled magneto-hydrodynamic equations in this paper. The proposed method is a first-order velocity correction projection algorithms in time marching, including standard velocity correction and rotation velocity correction, which can completely decouple all variables in the model. Meanwhile, the schemes are not only linear and only need to solve a series of linear partial differential equations with constant coefficients at each time step, but also the standard velocity correction algorithm can produce the Neumann boundary condition for the pressure field, but the rotational velocity correction algorithm can produce the consistent boundary which improve the accuracy of the pressure field. Thus, improving our computational efficiency. Then, we give the energy stability of the algorithms and give a detailed proofs. The key idea to establish the stability results of the rotation velocity correction algorithm is to transform the rotation term into a telescopic symmetric form by means of the Gauge–Uzawa formula. Finally, numerical experiments show that the rotation velocity correction projection algorithm is efficient to solve the thermally coupled magneto-hydrodynamic equations.https://www.mdpi.com/1099-4300/24/8/1159thermally coupled magneto-hydrodynamic equationsvelocity correction projection algorithmsdecouplingenergy stability |
| spellingShingle | Zhe Zhang Haiyan Su Xinlong Feng Linear Full Decoupling, Velocity Correction Method for Unsteady Thermally Coupled Incompressible Magneto-Hydrodynamic Equations Entropy thermally coupled magneto-hydrodynamic equations velocity correction projection algorithms decoupling energy stability |
| title | Linear Full Decoupling, Velocity Correction Method for Unsteady Thermally Coupled Incompressible Magneto-Hydrodynamic Equations |
| title_full | Linear Full Decoupling, Velocity Correction Method for Unsteady Thermally Coupled Incompressible Magneto-Hydrodynamic Equations |
| title_fullStr | Linear Full Decoupling, Velocity Correction Method for Unsteady Thermally Coupled Incompressible Magneto-Hydrodynamic Equations |
| title_full_unstemmed | Linear Full Decoupling, Velocity Correction Method for Unsteady Thermally Coupled Incompressible Magneto-Hydrodynamic Equations |
| title_short | Linear Full Decoupling, Velocity Correction Method for Unsteady Thermally Coupled Incompressible Magneto-Hydrodynamic Equations |
| title_sort | linear full decoupling velocity correction method for unsteady thermally coupled incompressible magneto hydrodynamic equations |
| topic | thermally coupled magneto-hydrodynamic equations velocity correction projection algorithms decoupling energy stability |
| url | https://www.mdpi.com/1099-4300/24/8/1159 |
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