A study of multiple solutions for the Navier-Stokes equations by a finite element method

H. Xu, P. Lin (Lead / Corresponding author), X. Si

Research output: Contribution to journalArticle

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 a 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).
Original language English 107-122 16 Numerical Mathematics: Theory, Methods and Applications 7 1 https://doi.org/10.4208/nmtma.2014.1236nm Published - 1 Feb 2014

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Multiple Solutions
Navier Stokes equations
Navier-Stokes Equations
Finite Element Method
Finite element method
Incompressible flow
Reynolds number
Homotopy Analysis Method
Similarity Transformation
Suction
Incompressible Flow
Analytic Solution
Restriction
Similarity

Cite this

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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 a 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).",
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In: Numerical Mathematics: Theory, Methods and Applications, Vol. 7, No. 1, 01.02.2014, p. 107-122.

Research output: Contribution to journalArticle

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