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 languageEnglish
    Pages (from-to)107-122
    Number of pages16
    JournalNumerical Mathematics: Theory, Methods and Applications
    Volume7
    Issue number1
    DOIs
    Publication statusPublished - 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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    TY - JOUR

    T1 - A study of multiple solutions for the Navier-Stokes equations by a finite element method

    AU - Xu, H.

    AU - Lin, P.

    AU - Si, X.

    PY - 2014/2/1

    Y1 - 2014/2/1

    N2 - 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).

    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 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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    EP - 122

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    JF - Numerical Mathematics: Theory, Methods and Applications

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