Volume 7, Issue 1
A Study of Multiple Solutions for the Navier-Stokes Equations by a Finite Element Method

Huanxia Xu, Ping Lin & Xinhui Si

Numer. Math. Theor. Meth. Appl., 7 (2014), pp. 107-122.

Published online: 2014-07

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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

Finite element method, Navier-Stokes equations, porous channel, expanding walls.

  • AMS Subject Headings

76M10, 76D05, 74H15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-7-107, author = {}, title = {A Study of Multiple Solutions for the Navier-Stokes Equations by a Finite Element Method}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2014}, volume = {7}, number = {1}, pages = {107--122}, 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).

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2014.1236nm}, url = {http://global-sci.org/intro/article_detail/nmtma/5867.html} }
TY - JOUR T1 - A Study of Multiple Solutions for the Navier-Stokes Equations by a Finite Element Method JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 107 EP - 122 PY - 2014 DA - 2014/07 SN - 7 DO - http://doi.org/10.4208/nmtma.2014.1236nm UR - https://global-sci.org/intro/article_detail/nmtma/5867.html KW - Finite element method, Navier-Stokes equations, porous channel, expanding walls. AB -

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).

Huanxia Xu, Ping Lin & Xinhui Si. (2020). A Study of Multiple Solutions for the Navier-Stokes Equations by a Finite Element Method. Numerical Mathematics: Theory, Methods and Applications. 7 (1). 107-122. doi:10.4208/nmtma.2014.1236nm
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