Semi-Discrete Energy-Stable Schemes for a Tensor-Based Hydrodynamic Model of Nematic Liquid Crystal Flows
DOI: 10.1007/S10915-016-0177-X
关键词: Complex fluid 、 Finite difference 、 Physics 、 Communication channel 、 Dissipation 、 Liquid crystal 、 Spacetime 、 Tensor 、 Statistical physics 、 Energy (signal processing)
摘要: In this paper, we develop a first-order and second-order coupled energy stable numerical scheme respectively for Q-tensor based hydrodynamic model of nematic liquid crystal flows. We then extend the first order to decoupled show that it is as well. The fully schemes are implemented in 2-dimensional space time, with which study defect dynamics flows crystals channel. shown be efficient solving model. methodology developed here also provides paradigm developing energy-stable more general models complex fluids obey an dissipation law.
springer.com
acm.org 
sci-hub.se 参考文章(35)
F.M. Leslie, Theory of Flow Phenomena in Liquid Crystals Advances in Liquid Crystals. ,vol. 4, pp. 1- 81 ,(1979) , 10.1016/B978-0-12-025004-2.50008-9
Xiao-Gang Yang, Qi Wang, M. Gregory Forest, Near equilibrium dynamics and one-dimensional spatial-temporal structures of polar active liquid crystals Chinese Physics B. ,vol. 23, pp. 118701- 118701 ,(2014) , 10.1088/1674-1056/23/11/118701
Masao Doi, Sam F Edwards, The theory of polymer dynamics Oxford University Press. ,(1986)
Francisco Guillén-González, María Ángeles Rodríguez-Bellido, Weak solutions for an initial–boundary Q-tensor problem related to liquid crystals Nonlinear Analysis-theory Methods & Applications. ,vol. 112, pp. 84- 104 ,(2015) , 10.1016/J.NA.2014.09.011
M. Gregory Forest, Qi Wang, Hydrodynamic theories for mixtures of polymers and rodlike liquid crystalline polymers. Physical Review E. ,vol. 72, pp. 041805- ,(2005) , 10.1103/PHYSREVE.72.041805
Daozhi Han, Xiaoming Wang, A second order in time, uniquely solvable, unconditionally stable numerical scheme for Cahn–Hilliard–Navier–Stokes equation Journal of Computational Physics. ,vol. 290, pp. 139- 156 ,(2015) , 10.1016/J.JCP.2015.02.046
N. Schopohl, T. J. Sluckin, Defect core structure in nematic liquid crystals. Physical Review Letters. ,vol. 59, pp. 2582- 2584 ,(1987) , 10.1103/PHYSREVLETT.59.2582
Marius Paicu, Arghir Zarnescu, Energy Dissipation and Regularity for a Coupled Navier–Stokes and Q-Tensor System Archive for Rational Mechanics and Analysis. ,vol. 203, pp. 45- 67 ,(2012) , 10.1007/S00205-011-0443-X
A.M Sonnet, P.L Maffettone, E.G Virga, Continuum theory for nematic liquid crystals with tensorial order Journal of Non-newtonian Fluid Mechanics. ,vol. 119, pp. 51- 59 ,(2004) , 10.1016/J.JNNFM.2003.02.001
Qi Wang, A hydrodynamic theory for solutions of nonhomogeneous nematic liquid crystalline polymers of different configurations Journal of Chemical Physics. ,vol. 116, pp. 9120- 9136 ,(2002) , 10.1063/1.1452722