An energy law preserving C0 finite element scheme for simulating the kinematic effects in liquid crystal flow dynamics

Ping Lin, Chun Liu, Hui Zhang

    Research output: Contribution to journalArticle

    52 Citations (Scopus)

    Abstract

    In this paper, we use finite element methods to simulate the hydrodynamical systems governing the motions of nematic liquid crystals in a bounded domain X. We reformulate the original model in the weak form which is consistent with the continuous dissipative energy law for the flow and director fields in W1;2þrðXÞ (r > 0 is an arbitrarily small number). This enables us to use convenient conformal C0 finite elements in solving the problem. Moreover, a discrete energy law is derived for a modified midpoint time discretization scheme. A fixed iterative method is used to solve the resulted nonlinear system so that a matrix free time evolution may be achieved and velocity and director variables may be solved separately. A number of hydrodynamical liquid crystal examples are computed to demonstrate the effects of the parameters and the performance of the method. c2007 Elsevier Inc. All rights reserved.
    Original languageEnglish
    Pages (from-to)1411-1427
    Number of pages17
    JournalJournal of Computational Physics
    Volume227
    Issue number2
    DOIs
    Publication statusPublished - Dec 2007

    Keywords

    • Liquid crystal flow
    • Non-Newtonian fluids
    • C0 finite element approximation
    • Discrete energy law
    • Singularity dynamics

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