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A Study of Multiple Solutions for the Navier-Stokes Equations by a Finite Element Method

Published online by Cambridge University Press:  28 May 2015

Huanxia Xu,
Ping Lin and
Xinhui Si
Huanxia Xu*
Affiliation:
Department of Mathematics and Mechanics, University of Science and Technology Beijing, Beijing 100083, China
Ping Lin*
Affiliation:
Department of Mathematics, University of Dundee, Dundee DD1 4HN, UK
Xinhui Si*
Affiliation:
Department of Mathematics and Mechanics, University of Science and Technology Beijing, Beijing 100083, China
*
Corresponding author.Email address:xuhuanxia568@163.com
Corresponding author.Email address:plin@maths.dundee.ac.uk
Corresponding author.Email address:xiaoniustu@163.com
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Abstract

In this paper, a finite element method is proposed to investigate multiple solutions of the Navier-Stokes equations for an unsteady, laminar, incompressible flow in a porous expanding channel. Dual or triple solutions for the fixed values of the wall suction Reynolds number R and the expansion ratio α are obtained numerically. The computed multiple solutions for the symmetric flow are validated by comparing them with approximate analytic solutions obtained by the similarity transformation and homotopy analysis method. Unlike previous works, our method deals with the Navier-Stokes equations directly and thus has no similarity and other restrictions as in previous works. Finally we use the method to study multiple solutions for three cases of the asymmetric flow (which has not been studied before using the similarity-type techniques).

Keywords

76M1076D0574H15Finite element methodNavier-Stokes equationsporous channelexpanding walls

Information

Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 7 , Issue 1 , February 2014, pp. 107 - 122
Copyright
Copyright © Global Science Press Limited 2014

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