Open Access
2014 Stabilized Discretization in Spline Element Method for Solution of Two-Dimensional Navier-Stokes Problems
Neng Wan, Ke Du, Tao Chen, Sentang Zhang, Gongnan Xie
Abstr. Appl. Anal. 2014(SI04): 1-11 (2014). DOI: 10.1155/2014/350682


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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Neng Wan. Ke Du. Tao Chen. Sentang Zhang. Gongnan Xie. "Stabilized Discretization in Spline Element Method for Solution of Two-Dimensional Navier-Stokes Problems." Abstr. Appl. Anal. 2014 (SI04) 1 - 11, 2014.


Published: 2014
First available in Project Euclid: 27 February 2015

zbMATH: 07022205
MathSciNet: MR3256244
Digital Object Identifier: 10.1155/2014/350682

Rights: Copyright © 2014 Hindawi

Vol.2014 • No. SI04 • 2014
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