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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 | Citation: | 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 |
Appears in Collections: | Staff Publications |
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