In this paper, we use finite element methods to simulate the hydrodynamical systems governing the motions of nematic liquid crystals in a bounded domain X. 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;2þrðXÞ (r > 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. c2007 Elsevier Inc. All rights reserved.
- Liquid crystal flow
- Non-Newtonian fluids
- C0 finite element approximation
- Discrete energy law
- Singularity dynamics