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: Neng Wan, Ke Du, Tao Chen, Sentang Zhang, Gongnan Xie
Format: Article
Language:English
Published: Wiley 2014-01-01
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.
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institution OA Journals
issn 1085-3375
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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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