一种线性、解耦且能量稳定的Smectic-A液晶流数值方案
A Linear, Decoupled and Energy stable scheme for smectic-A Liquid Crystal Flows
AI总结：
本文提出一种线性、解耦且能量稳定的数值方案，用于求解Smectic-A液晶流模型，该方案能有效处理非线性耦合问题，并通过严格证明验证了能量耗散特性。
摘要：
本文考虑了Smectic-A液晶流模型的数值近似。该模型方程源自de Gennes自由能的变分方法，是一个高度非线性的系统，耦合了不可压缩纳维-斯托克斯方程和两个非线性耦合的二阶椭圆方程。基于对非线性项的巧妙显式-隐式处理，我们开发了一种无条件能量稳定的、线性和解耦的时间推进数值方案。我们还严格证明了所提出方案在离散水平上遵循能量耗散定律。各种数值模拟展示了该方案的准确性和稳定性。
英文摘要：
In this paper, we consider numerical approximations for the model of smectic-A liquid crystal flows. The model equation, that is derived from the variational approach of the de Gennes free energy, is a highly nonlinear system that couples the incompressible Navier-Stokes equations, and two nonlinear coupled second-order elliptic equations. Based on some subtle explicit--implicit treatments for nonlinear terms, we develop a unconditionally energy stable, linear and decoupled time marching numerical scheme. We also rigorously prove that the proposed scheme obeys the energy dissipation law at the discrete level. Various numerical simulations are presented to demonstrate the accuracy and the stability thereafter.
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