Publications › Journal article · 2017
A novel linear, second order, unconditionally energy-stable scheme for a hydrodynamic Q-tensor model for liquid crystals
Computer Methods in Applied Mechanics and Engineering, 318, 803-825, 2017.
Abstract
The hydrodynamic -tensor model has been widely used for studying flows of liquid crystals and liquid crystal polymers. It is derived from a variational approach together with the generalized Onsager principle, in which the total energy decreases in time. In this paper, we develop a novel, linear, second order semi-discrete scheme in time to solve the governing system. The scheme is developed following the so called ``energy quadratization" technique so that it is linear and unconditionally energy stable at the semi-discrete level. This scheme is further discretized in space using a second order finite difference method and implemented on a GPU for high performance computing. The convergence rate in time is established using a mesh refinement test. Several numerical examples are presented to demonstrate the effectiveness of the model and the numerical scheme in simulating defect dynamics in flows of liquid crystals.
Cite
@article{zhao2017nls,
author = {Zhao, J. and Yang, X. and Gong, Y. and Wang, Q.},
title = {A novel linear, second order, unconditionally energy-stable scheme for a hydrodynamic $Q$-tensor model for liquid crystals},
journal = {Computer Methods in Applied Mechanics and Engineering},
volume = {318},
pages = {803-825},
year = {2017},
doi = {10.1016/j.cma.2017.01.031},
}Author marks: * corresponding, △ co-first, ♠ graduate student, ♣ undergraduate student, ♡ postdoc, at the time of the work.