ENERGY STABLE NUMERICAL SCHEMES FOR A HYDRODYNAMIC MODEL OF NEMATIC LIQUID CRYSTALS

被引：75

作者：

Zhao, Jia ^{[1
,2
]}

Yang, Xiaofeng ^{[1
]}

Li, Jun ^{[3
]}

Wang, Qi ^{[3
,4
,5
,6
]}

机构：

[1] Univ South Carolina, Dept Math, Columbia, SC 29208 USA

[2] Univ N Carolina, Dept Math, Chapel Hill, NC 27599 USA

[3] Nankai Univ, Sch Math, Tianjin 300071, Peoples R China

[4] Beijing Computat Sci Res Ctr, Beijing 100931, Peoples R China

[5] Univ South Carolina, Dept Math, IMI, Columbia, SC 29208 USA

[6] Univ South Carolina, NanoCtr, Columbia, SC 29208 USA

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2016年 / 38卷 / 05期

基金：

美国国家科学基金会;

关键词：

liquid crystals; energy stable schemes; finite difference; hydrodynamics; phase field theory; ALLEN-CAHN; APPROXIMATIONS; 2ND-ORDER; EQUATIONS; FLOWS; TIME;

D O I：

10.1137/15M1024093

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We develop a first-order and a second-order, coupled, energy stable numerical schemes for a modified Ericksen-Leslie hydrodynamic model for nematic liquid crystals. We then discuss two ways to develop decoupled schemes for the model and show that they are energy stable as well. The coupled schemes are implemented in 2-dimensional space, with which we study defect dynamics in flows of nematic liquid crystals. Comparisons of our model predictions with that of a reduced model previously studied, which used the material derivative in place of the time invariant derivative in the Ericksen-Leslie model, are made, demonstrating quite different, but more realistic orientational dynamics in flows of nematic liquid crystals.

引用

页码：A3264 / A3290

页数：27

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