Simulations of singularity dynamics in liquid crystal flows: a C0 finite element approach

Ping Lin, Chun Liu

    Research output: Contribution to journalArticle

    46 Citations (Scopus)

    Abstract

    In this paper, we present a C0 finite element method for a 2D hydrodynamic liquid crystal model which is simpler than existing C1 element methods and mixed element formulation. The energy law is formally justified and the energy decay is used as a validation tool for our numerical computation. A splitting method combined with only a few fixed point iteration for the penalty term of the director field is applied to reduce the size of the stiffness matrix and to keep the stiffness matrix time-independent. The latter avoids solving a linear system at every time step and largely reduces the computational time, especially when direct linear system solvers are used. Our approach is verified by comparing its computational results with those obtained by C1 elements and by mixed formulation. Through numerical experiments of a few other splittings and explicit–implicit strategies, we recommend a fast and reliable algorithm for this model. A number of examples are computed to demonstrate the algorithm.
    Original languageEnglish
    Pages (from-to)348-362
    Number of pages15
    JournalJournal of Computational Physics
    Volume215
    Issue number1
    DOIs
    Publication statusPublished - Jun 2006

    Keywords

    • Liquid crystal flow
    • Finite element approximation
    • Splitting methods

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