Abstract We consider in this paper numerical approximations for the hydro-dynamically coupled phase-field model for an immiscible binary mixture of passive/active nematic Liquid Crystals (LCs) and viscous fluids. The passive model is a highly coupled nonlinear system that consists of the incompressible Navier-Stokes equations, the Cahn-Hilliard equations, and the constitutive equation for the polarization field. The active model can be viewed as an assembly of a passive part and a phenomenological active part. We then construct an efficient and linear time marching scheme to solve the passive model and further extend it to solve the active model. Various numerical simulations are presented to demonstrate the stability and accuracy of the proposed scheme in simulating some simulations in 2D and 3D, including the drop deformation dynamics and spinodal decompositions.

中文翻译：

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被动/主动向列液晶和粘性流体的二元混合物的流体动力耦合相场模型的数值近似

摘要 我们在本文中考虑了被动/主动向列液晶 (LC) 和粘性流体的不混溶二元混合物的流体动力耦合相场模型的数值近似。无源模型是一个高度耦合的非线性系统，由不可压缩的 Navier-Stokes 方程、Cahn-Hilliard 方程和极化场的本构方程组成。主动模型可以看作是被动部分和现象学主动部分的组合。然后我们构建了一个高效的线性时间推进方案来解决被动模型，并进一步扩展它来解决主动模型。提出了各种数值模拟，以证明所提出的方案在模拟 2D 和 3D 中的一些模拟时的稳定性和准确性，