Stabilized Discretization in Spline Element Method for Solution of Two-Dimensional Navier-Stokes Problems
In terms of the poor geometric adaptability of spline element method, a geometric precision spline method, which uses the rational Bezier patches to indicate the solution domain, is proposed for two-dimensional viscous uncompressed Navier-Stokes equation. Besides fewer pending unknowns, higher accur...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/350682 |
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| author | Neng Wan Ke Du Tao Chen Sentang Zhang Gongnan Xie |
| author_facet | Neng Wan Ke Du Tao Chen Sentang Zhang Gongnan Xie |
| author_sort | Neng Wan |
| collection | DOAJ |
| description | In terms of the poor geometric adaptability of spline element method, a geometric precision spline method, which uses the rational Bezier patches to indicate the solution domain, is proposed for two-dimensional viscous uncompressed Navier-Stokes equation. Besides fewer pending unknowns, higher accuracy, and computation efficiency, it possesses such advantages as accurate representation of isogeometric analysis for object boundary and the unity of geometry and analysis modeling. Meanwhile, the selection of B-spline basis functions and the grid definition is studied and a stable discretization format satisfying inf-sup conditions is proposed. The degree of spline functions approaching the velocity field is one order higher than that approaching pressure field, and these functions are defined on one-time refined grid. The Dirichlet boundary conditions are imposed through the Nitsche variational principle in weak form due to the lack of interpolation properties of the B-splines functions. Finally, the validity of the proposed method is verified with some examples. |
| format | Article |
| id | doaj-art-1382e47629524c5bbdc39edddd9c37de |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-1382e47629524c5bbdc39edddd9c37de2025-08-20T02:04:49ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/350682350682Stabilized Discretization in Spline Element Method for Solution of Two-Dimensional Navier-Stokes ProblemsNeng Wan0Ke Du1Tao Chen2Sentang Zhang3Gongnan Xie4Key Laboratory of Contemporary Design and Integrated Manufacturing Technology, Ministry of Education, Northwestern Polytechnical University, Xi’an 710072, ChinaKey Laboratory of Contemporary Design and Integrated Manufacturing Technology, Ministry of Education, Northwestern Polytechnical University, Xi’an 710072, ChinaKey Laboratory of Contemporary Design and Integrated Manufacturing Technology, Ministry of Education, Northwestern Polytechnical University, Xi’an 710072, ChinaAVIC Shenyang Liming Aeroengine Group Corporation Ltd., Shenyang 110043, ChinaKey Laboratory of Contemporary Design and Integrated Manufacturing Technology, Ministry of Education, Northwestern Polytechnical University, Xi’an 710072, ChinaIn terms of the poor geometric adaptability of spline element method, a geometric precision spline method, which uses the rational Bezier patches to indicate the solution domain, is proposed for two-dimensional viscous uncompressed Navier-Stokes equation. Besides fewer pending unknowns, higher accuracy, and computation efficiency, it possesses such advantages as accurate representation of isogeometric analysis for object boundary and the unity of geometry and analysis modeling. Meanwhile, the selection of B-spline basis functions and the grid definition is studied and a stable discretization format satisfying inf-sup conditions is proposed. The degree of spline functions approaching the velocity field is one order higher than that approaching pressure field, and these functions are defined on one-time refined grid. The Dirichlet boundary conditions are imposed through the Nitsche variational principle in weak form due to the lack of interpolation properties of the B-splines functions. Finally, the validity of the proposed method is verified with some examples.http://dx.doi.org/10.1155/2014/350682 |
| spellingShingle | Neng Wan Ke Du Tao Chen Sentang Zhang Gongnan Xie Stabilized Discretization in Spline Element Method for Solution of Two-Dimensional Navier-Stokes Problems Abstract and Applied Analysis |
| title | Stabilized Discretization in Spline Element Method for Solution of Two-Dimensional Navier-Stokes Problems |
| title_full | Stabilized Discretization in Spline Element Method for Solution of Two-Dimensional Navier-Stokes Problems |
| title_fullStr | Stabilized Discretization in Spline Element Method for Solution of Two-Dimensional Navier-Stokes Problems |
| title_full_unstemmed | Stabilized Discretization in Spline Element Method for Solution of Two-Dimensional Navier-Stokes Problems |
| title_short | Stabilized Discretization in Spline Element Method for Solution of Two-Dimensional Navier-Stokes Problems |
| title_sort | stabilized discretization in spline element method for solution of two dimensional navier stokes problems |
| url | http://dx.doi.org/10.1155/2014/350682 |
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