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

Ping Lin, Chun Liu, Hui Zhang

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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
Issue number2
StatePublished - Dec 10 2007

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

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