A three-stage operator-splitting/finite element method for the numerical simulation of liquid crystal flow

Roland Glowinski, Ping Lin, Xing-Bin Pan

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    In this article, we investigate the application of an operator-splitting/finite element method to the numerical simulation of a liquid crystal flow. The operator-splitting is achieved through three stages, so that each stage is simpler and easier to deal with than the step of any un-split implicit scheme. The first stage deals with the system coupling a Stokes equation for velocity with an equation modeling the diffusion of the liquid crystal director field. The second stage deals with the convection of both the velocity and director field; a wave-like equation approach is used to treat this advection part and proves being quite efficient. Finally, the third stage deals with the nonlinear terms; a (quasi) closed form solution can be derived for this stage. Overall, with this type of splitting, the nonlinear terms in the liquid crystal model can be treated quite easily. The results of several numerical experiments show the good performances of the three-stage splitting method discussed in this article.
    Original languageEnglish
    Pages (from-to)440-454
    Number of pages15
    JournalInternational Journal of Numerical Analysis and Modeling
    Volume6
    Issue number3
    Publication statusPublished - 2009

    Fingerprint

    Operator Splitting
    Splitting Method
    Liquid Crystal
    Liquid crystals
    Mathematical operators
    Finite Element Method
    Finite element method
    Numerical Simulation
    Computer simulation
    Implicit Scheme
    Stokes Equations
    Advection
    Term
    Closed-form Solution
    Convection
    Numerical Experiment
    Modeling
    Experiments
    Model

    Keywords

    • Finite element method
    • Operator-splitting method
    • Liquid crystal flow

    Cite this

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    title = "A three-stage operator-splitting/finite element method for the numerical simulation of liquid crystal flow",
    abstract = "In this article, we investigate the application of an operator-splitting/finite element method to the numerical simulation of a liquid crystal flow. The operator-splitting is achieved through three stages, so that each stage is simpler and easier to deal with than the step of any un-split implicit scheme. The first stage deals with the system coupling a Stokes equation for velocity with an equation modeling the diffusion of the liquid crystal director field. The second stage deals with the convection of both the velocity and director field; a wave-like equation approach is used to treat this advection part and proves being quite efficient. Finally, the third stage deals with the nonlinear terms; a (quasi) closed form solution can be derived for this stage. Overall, with this type of splitting, the nonlinear terms in the liquid crystal model can be treated quite easily. The results of several numerical experiments show the good performances of the three-stage splitting method discussed in this article.",
    keywords = "Finite element method, Operator-splitting method, Liquid crystal flow",
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    A three-stage operator-splitting/finite element method for the numerical simulation of liquid crystal flow. / Glowinski, Roland; Lin, Ping; Pan, Xing-Bin.

    In: International Journal of Numerical Analysis and Modeling, Vol. 6, No. 3, 2009, p. 440-454.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - A three-stage operator-splitting/finite element method for the numerical simulation of liquid crystal flow

    AU - Glowinski, Roland

    AU - Lin, Ping

    AU - Pan, Xing-Bin

    PY - 2009

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    N2 - In this article, we investigate the application of an operator-splitting/finite element method to the numerical simulation of a liquid crystal flow. The operator-splitting is achieved through three stages, so that each stage is simpler and easier to deal with than the step of any un-split implicit scheme. The first stage deals with the system coupling a Stokes equation for velocity with an equation modeling the diffusion of the liquid crystal director field. The second stage deals with the convection of both the velocity and director field; a wave-like equation approach is used to treat this advection part and proves being quite efficient. Finally, the third stage deals with the nonlinear terms; a (quasi) closed form solution can be derived for this stage. Overall, with this type of splitting, the nonlinear terms in the liquid crystal model can be treated quite easily. The results of several numerical experiments show the good performances of the three-stage splitting method discussed in this article.

    AB - In this article, we investigate the application of an operator-splitting/finite element method to the numerical simulation of a liquid crystal flow. The operator-splitting is achieved through three stages, so that each stage is simpler and easier to deal with than the step of any un-split implicit scheme. The first stage deals with the system coupling a Stokes equation for velocity with an equation modeling the diffusion of the liquid crystal director field. The second stage deals with the convection of both the velocity and director field; a wave-like equation approach is used to treat this advection part and proves being quite efficient. Finally, the third stage deals with the nonlinear terms; a (quasi) closed form solution can be derived for this stage. Overall, with this type of splitting, the nonlinear terms in the liquid crystal model can be treated quite easily. The results of several numerical experiments show the good performances of the three-stage splitting method discussed in this article.

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    KW - Operator-splitting method

    KW - Liquid crystal flow

    M3 - Article

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    SP - 440

    EP - 454

    JO - International Journal of Numerical Analysis and Modeling

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