Solving the Incompressible Surface Stokes Equation by Standard Velocity-Correction Projection Methods
In this paper, an effective numerical algorithm for the Stokes equation of a curved surface is presented and analyzed. The velocity field was decoupled from the pressure by the standard velocity correction projection method, and the penalty term was introduced to make the velocity satisfy the tangen...
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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/1099-4300/24/10/1338 |
| _version_ | 1797473487732867072 |
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| author | Yanzi Zhao Xinlong Feng |
| author_facet | Yanzi Zhao Xinlong Feng |
| author_sort | Yanzi Zhao |
| collection | DOAJ |
| description | In this paper, an effective numerical algorithm for the Stokes equation of a curved surface is presented and analyzed. The velocity field was decoupled from the pressure by the standard velocity correction projection method, and the penalty term was introduced to make the velocity satisfy the tangential condition. The first-order backward Euler scheme and second-order BDF scheme are used to discretize the time separately, and the stability of the two schemes is analyzed. The mixed finite element pair <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>P</mi><mn>2</mn></msub><mo>,</mo><msub><mi>P</mi><mn>1</mn></msub><mo>)</mo></mrow></semantics></math></inline-formula> is applied to discretization of space. Finally, numerical examples are given to verify the accuracy and effectiveness of the proposed method. |
| first_indexed | 2024-03-09T20:15:11Z |
| format | Article |
| id | doaj.art-16d9019616624ff58a491c68af3bbc20 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T20:15:11Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
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| series | Entropy |
| spelling | doaj.art-16d9019616624ff58a491c68af3bbc202023-11-24T00:01:58ZengMDPI AGEntropy1099-43002022-09-012410133810.3390/e24101338Solving the Incompressible Surface Stokes Equation by Standard Velocity-Correction Projection MethodsYanzi Zhao0Xinlong Feng1College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, ChinaIn this paper, an effective numerical algorithm for the Stokes equation of a curved surface is presented and analyzed. The velocity field was decoupled from the pressure by the standard velocity correction projection method, and the penalty term was introduced to make the velocity satisfy the tangential condition. The first-order backward Euler scheme and second-order BDF scheme are used to discretize the time separately, and the stability of the two schemes is analyzed. The mixed finite element pair <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>P</mi><mn>2</mn></msub><mo>,</mo><msub><mi>P</mi><mn>1</mn></msub><mo>)</mo></mrow></semantics></math></inline-formula> is applied to discretization of space. Finally, numerical examples are given to verify the accuracy and effectiveness of the proposed method.https://www.mdpi.com/1099-4300/24/10/1338incompressible Stokes equation for surfacesstandard velocity correction projection methodmixed finite element pairpenalty term |
| spellingShingle | Yanzi Zhao Xinlong Feng Solving the Incompressible Surface Stokes Equation by Standard Velocity-Correction Projection Methods Entropy incompressible Stokes equation for surfaces standard velocity correction projection method mixed finite element pair penalty term |
| title | Solving the Incompressible Surface Stokes Equation by Standard Velocity-Correction Projection Methods |
| title_full | Solving the Incompressible Surface Stokes Equation by Standard Velocity-Correction Projection Methods |
| title_fullStr | Solving the Incompressible Surface Stokes Equation by Standard Velocity-Correction Projection Methods |
| title_full_unstemmed | Solving the Incompressible Surface Stokes Equation by Standard Velocity-Correction Projection Methods |
| title_short | Solving the Incompressible Surface Stokes Equation by Standard Velocity-Correction Projection Methods |
| title_sort | solving the incompressible surface stokes equation by standard velocity correction projection methods |
| topic | incompressible Stokes equation for surfaces standard velocity correction projection method mixed finite element pair penalty term |
| url | https://www.mdpi.com/1099-4300/24/10/1338 |
| work_keys_str_mv | AT yanzizhao solvingtheincompressiblesurfacestokesequationbystandardvelocitycorrectionprojectionmethods AT xinlongfeng solvingtheincompressiblesurfacestokesequationbystandardvelocitycorrectionprojectionmethods |