SECOND ORDER, LINEAR, AND UNCONDITIONALLY ENERGY STABLE SCHEMES FOR A HYDRODYNAMIC MODEL OF SMECTIC-A LIQUID CRYSTALS
SECOND ORDER, LINEAR, AND UNCONDITIONALLY ENERGY STABLE SCHEMES FOR A HYDRODYNAMIC MODEL OF SMECTIC-A LIQUID CRYSTALS
复制标题
近晶-A 液晶流体动力学模型的二阶、线性和无条件能量稳定方案
DOI：
10.1137/17m1119834
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发表时间：
2017-01-01
影响因子：
3.1
通讯作者：
Zhang, Hui
中科院分区：
文献类型：
--
作者：
Chen, Rui;Yang, Xiaofeng;Zhang, Hui
本文考虑近晶A型液晶流体动力学模型的数值近似。该模型是一个高度非线性的系统，耦合不可压缩的Navier-Stokes方程和层变量的本构方程，来自于修改的Oseen-Frank能量的变分方法。我们开发了两个线性的，二阶时间推进计划的基础上的非线性项的本构方程，Navier-Stokes方程的投影方法，和一些微妙的隐式显式处理的对流和应力项的不变能量平方法。此外，我们严格证明了线性系统的适定性和它们的无条件能量稳定性。各种数值实验，以证明在模拟剪切流和磁场下的动力学的数值方案的稳定性和准确性。
In this paper, we consider the numerical approximations for a hydrodynamical model of smectic-A liquid crystals. The model, derived from the variational approach of the modified Oseen--Frank energy, is a highly nonlinear system that couples the incompressible Navier--Stokes equations and a constitutive equation for the layer variable. We develop two linear, second order time marching schemes based on the Invariant Energy Quadratization method for nonlinear terms in the constitutive equation, the projection method for the Navier--Stokes equations, and some subtle implicit-explicit treatments for the convective and stress terms. Moreover, we prove the well-posedness of the linear system and their unconditionally energy stabilities rigorously. Various numerical experiments are presented to demonstrate the stability and the accuracy of the numerical schemes in simulating the dynamics under shear flow and the magnetic field.