Commun. Comput. Phys., 9 (2011), pp. 974-993.


Numerical Simulations of Hydrodynamics of Nematic Liquid Crystals: Effects of Kinematic Transports

Shupeng Zhang 1, Chun Liu 2, Hui Zhang 1*

1 School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China.
2 Department of Mathematics, Pennsylvania State University, University Park, PA 18601, USA.

Received 16 January 2010; Accepted (in revised version) 29 June 2010
Available online 2 November 2010
doi:10.4208/cicp.160110.290610a

Abstract

In this paper, we investigate the effects of kinematic transports on the nematic liquid crystal system numerically and theoretically. The model we used is a "1+2" elastic continuum model simplified from the Ericksen-Leslie system. The numerical experiments are carried out by using a Legendre-Galerkin spectral method which can preserve the energy law in the discrete form. Based on this highly accurate numerical approach we find some interesting and important relationships between the kinematic transports and the characteristics of the flow. We make some analysis to explain these results. Several significant scaling properties are also verified by our simulations.

AMS subject classifications: 65M70, 76A15
Key words: Nematic liquid crystals, kinematic transports, Legendre-Galerkin spectral method, tumbling, flow-aligning.

*Corresponding author.
Email: shupeng.zhang@gmail.com (S. Zhang), liu@math.psu.edu (C. Liu), hzhang@bnu.edu.cn (H. Zhang)
 

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