We consider in this paper numerical approximations of the immiscible binary mixture of nematic liquid crystals (LCs) and viscous fluids. We develop a second-order time marching scheme by adopting the recently developed stabilized-SAV (scalar auxiliary variable) approach where several critical stabilization terms are added to enhance the stability; thus, large time steps are allowed in computations. The scheme is highly efficient and one only needs to solve several decoupled linear equations with constant coefficients at each time step. The energy stability of the scheme is proved, and various 2D and 3D numerical experiments including the drop deformations and phase separations are then performed to validate the accuracy and energy stability of the proposed scheme.

我们在本文中考虑了向列液晶（LCs）和粘性流体的不混溶二元混合物的数值近似。通过采用最近开发的稳定化SAV（标量辅助变量）方法，我们开发了一个二阶时间行进方案，其中添加了几个关键的稳定项以增强稳定性。因此，在计算中允许较大的时间步长。该方案是高效的，并且只需要在每个时间步求解具有恒定系数的几个解耦线性方程式即可。证明了该方案的能量稳定性，然后进行了各种2D和3D数值实验，包括液滴变形和相分离，以验证所提出方案的准确性和能量稳定性。