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

  • Authors:

  • Ping Lin;Chun Liu;Hui Zhang

  • Affiliations:

  • Department of Mathematics, The National University of Singapore, Singapore 117543, Singapore;Department of Mathematics, Pennsylvania State University, University Park, PA 18601, USA;School of Mathematical Sciences, Beijing Normal University, Beijing 100875, PR China

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2007

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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 @W. 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 W^1^,^2^+^@s(@W) (@s0 is an arbitrarily small number). This enables us to use convenient conformal C^0 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.