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Local RBFs Based Collocation Methods for Unsteady Navier-Stokes Equations

Published online by Cambridge University Press:  29 May 2015

Xueying Zhang ,
Xin An  and
C. S. Chen
Xueying Zhang*
Affiliation:
College of Science, Hohai University, Nanjing, Jiangsu 210098, China
Xin An
Affiliation:
College of Science, Hohai University, Nanjing, Jiangsu 210098, China
C. S. Chen
Affiliation:
Department of Mathematics, University of Southern Mississippi, Hattiesburg, MS 39406, U.S.A Department of Engineering Mechanics, Hohai University, Nanjing, Jiangsu 210098, China
*
*Corresponding author. Email: zhangxy.math@gmail.com (X. Y. Zhang)
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Abstract

The local RBFs based collocation methods (LRBFCM) is presented to solve two-dimensional incompressible Navier-Stokes equations. In avoiding the ill-conditioned problem, the weight coefficients of linear combination with respect to the function values and its derivatives can be obtained by solving low-order linear systems within local supporting domain. Then, we reformulate local matrix in the global and sparse matrix. The obtained large sparse linear systems can be directly solved instead of using more complicated iterative method. The numerical experiments have shown that the developed LRBFCM is suitable for solving the incompressible Navier-Stokes equations with high accuracy and efficiency.

Keywords

65M1035L03Navier-Stokes equationslocal collocation methodparticular solutionsradial basis functions (RBFs)large sparse linear systems
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 7 , Issue 4 , August 2015 , pp. 430 - 440
Copyright
Copyright © Global-Science Press 2015 

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