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 (https://doi.org/10.1137/130923683)
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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.
ORCID iDs
MacDonald, Craig S. ORCID: https://orcid.org/0000-0002-9996-674X, MacKenzie, John A. ORCID: https://orcid.org/0000-0003-4412-7057, Ramage, Alison ORCID: https://orcid.org/0000-0003-4709-0691 and Newton, Christopher J. P.;-
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Item type: Article ID code: 51133 Dates: DateEvent11 March 2015Published19 December 2014AcceptedNotes: © 2015, Society for Industrial and Applied Mathematics Subjects: Science > Mathematics > Probabilities. Mathematical statistics
Science > Mathematics > Electronic computers. Computer scienceDepartment: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 16 Jan 2015 14:03 Last modified: 12 Oct 2024 00:20 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/51133