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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 451546, 7 pages
http://dx.doi.org/10.1155/2014/451546
Research Article

Numerical Modeling of Stokes Flow in a Circular Cavity by Variational Multiscale Element Free Galerkin Method

College of Science, China Three Gorges University, Yichang 443002, China

Received 31 May 2014; Accepted 21 July 2014; Published 14 August 2014

Academic Editor: Alex Elías-Zúñiga

Copyright © 2014 Ping Zhang and Xiaohua Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The variational multiscale element free Galerkin method is extended to simulate the Stokes flow problems in a circular cavity as an irregular geometry. The method is combined with Hughes’s variational multiscale formulation and element free Galerkin method; thus it inherits the advantages of variational multiscale and meshless methods. Meanwhile, a simple technique is adopted to impose the essential boundary conditions which makes it easy to solve problems with complex area. Finally, two examples are solved and good results are obtained as compared with solutions of analytical and numerical methods, which demonstrates that the proposed method is an attractive approach for solving incompressible fluid flow problems in terms of accuracy and stability, even for complex irregular boundaries.