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

Ping Lin, Chun Liu, Hui Zhang

Research output: Contribution to journalArticle

50 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 Ω. 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, 2 + σ (Ω) (σ > 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.

Original languageEnglish (US)
Pages (from-to)1411-1427
Number of pages17
JournalJournal of Computational Physics
Volume227
Issue number2
DOIs
StatePublished - Dec 10 2007

Fingerprint

Nematic liquid crystals
Iterative methods
Liquid crystals
preserving
Nonlinear systems
Kinematics
kinematics
liquid crystals
Finite element method
nonlinear systems
flow distribution
finite element method
energy
matrices

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

Cite this

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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 Ω. 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, 2 + σ (Ω) (σ > 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.",
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An energy law preserving C0 finite element scheme for simulating the kinematic effects in liquid crystal dynamics. / Lin, Ping; Liu, Chun; Zhang, Hui.

In: Journal of Computational Physics, Vol. 227, No. 2, 10.12.2007, p. 1411-1427.

Research output: Contribution to journalArticle

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