Energy Stable Numerical Schemes for a Hydrodynamic Model of Nematic Liquid Crystals
Energy Stable Numerical Schemes for a Hydrodynamic Model of Nematic Liquid Crystals
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DOI：
10.1137/15m1024093
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发表时间：
2016-10
期刊：
影响因子：
--
通讯作者：
Jia Zhao;Xiaofeng Yang;Jun Yu Li;Qi Wang
中科院分区：
文献类型：
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作者：
Jia Zhao;Xiaofeng Yang;Jun Yu Li;Qi Wang
我们为向列液晶的改进Ericksen- Leslie流体动力学模型建立了一阶和二阶耦合的能量稳定数值格式。然后，我们讨论了两种开发模型解耦方案的方法，并表明它们也是能量稳定的。耦合格式在二维空间中实现，用于研究向列型液晶流动中的缺陷动力学。我们的模型预测与先前研究的简化模型的预测进行了比较，该模型使用Ericksen- Leslie模型中的材料导数代替时不变导数，展示了完全不同的，但更现实的向列液晶流动中的定向动力学。
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.