Efficient moving mesh methods for Q-tensor models of nematic liquid crystals

MacDonald, Craig S. and MacKenzie, John A. and Ramage, Alison and Newton, Christopher J. P. (2015) Efficient moving mesh methods for Q-tensor models of nematic liquid crystals. SIAM Journal on Scientific Computing, 37 (2). B215-B238. ISSN 1064-8275

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    Abstract

    This paper describes a robust and efficient numerical scheme for solving the system of six coupled partial differential equations which arises when using Q-tensor theory to model the behaviour of a nematic liquid crystal cell under the influence of an applied electric field. The key novel feature is the use of a full moving mesh partial differential equation (MMPDE) approach to generate an adaptive mesh which accurately resolves important solution features. This includes the use of a new monitor function based on a local measure of biaxiality. In addition, adaptive time-step control is used to ensure the accurate predicting of the switching time, which is often critical in the design of liquid crystal cells. We illustrate the behaviour of the method on a one-dimensional time-dependent problem in a Pi-cell geometry which admits two topologically different equilibrium states, modelling the order reconstruction which occurs on the application of an electric field. Our numerical results show that, as well as achieving optimal rates of convergence in space and time, we obtain higher levels of solution accuracy and a considerable improvement in computational efficiency compared to other moving mesh methods used previously for liquid crystal problems.

    Creators(s): MacDonald, Craig S. ORCID logoORCID: https://orcid.org/0000-0002-9996-674X, MacKenzie, John A. ORCID logoORCID: https://orcid.org/0000-0003-4412-7057, Ramage, Alison ORCID logoORCID: https://orcid.org/0000-0003-4709-0691 and Newton, Christopher J. P.;
    Item type:Article
    ID code:51133
    Notes:© 2015, Society for Industrial and Applied Mathematics
    Keywords:moving mesh analysis, moving mesh, nematic liquid crystal, Probabilities. Mathematical statistics, Electronic computers. Computer science, Computational Mathematics, Applied Mathematics
    Subjects:Science > Mathematics > Probabilities. Mathematical statistics
    Science > Mathematics > Electronic computers. Computer science
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:16 Jan 2015 14:03
    Last modified:06 Mar 2021 02:01
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/51133
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