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

Craig S. MacDonald, John A. MacKenzie, Alison Ramage, Christopher J. P. Newton

Research output: Contribution to journalArticle

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119 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)B215-B238
Number of pages24
JournalSIAM Journal on Scientific Computing
Volume37
Issue number2
DOIs
Publication statusPublished - 11 Mar 2015

Fingerprint

Moving Mesh Method
Nematic liquid crystals
Nematic Liquid Crystal
Liquid crystals
Partial differential equations
Tensors
Tensor
Electric fields
Liquid Crystal
Electric Field
Cell
Partial differential equation
Computational efficiency
Moving Mesh
Adaptive Mesh
Optimal Rate of Convergence
Pi
Equilibrium State
Computational Efficiency
Numerical Scheme

Keywords

  • moving mesh analysis
  • moving mesh
  • nematic liquid crystal

Cite this

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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.",
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Efficient moving mesh methods for Q-tensor models of nematic liquid crystals. / MacDonald, Craig S.; MacKenzie, John A.; Ramage, Alison; Newton, Christopher J. P.

In: SIAM Journal on Scientific Computing, Vol. 37, No. 2, 11.03.2015, p. B215-B238.

Research output: Contribution to journalArticle

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