Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.jcp.2007.09.005
Title: An energy law preserving C0 finite element scheme for simulating the kinematic effects in liquid crystal dynamics
Authors: Lin, P. 
Liu, C.
Zhang, H.
Keywords: C0 finite element approximation
Discrete energy law
Liquid crystal flow
Non-Newtonian fluids
Singularity dynamics
Issue Date: 10-Dec-2007
Source: Lin, P., Liu, C., Zhang, H. (2007-12-10). An energy law preserving C0 finite element scheme for simulating the kinematic effects in liquid crystal dynamics. Journal of Computational Physics 227 (2) : 1411-1427. ScholarBank@NUS Repository. https://doi.org/10.1016/j.jcp.2007.09.005
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. © 2007 Elsevier Inc. All rights reserved.
Source Title: Journal of Computational Physics
URI: http://scholarbank.nus.edu.sg/handle/10635/102833
ISSN: 00219991
DOI: 10.1016/j.jcp.2007.09.005
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