In this work, we present three linear numerical schemes to model nematic liquid crystals using the Landau-de Gennes $\textbf{Q}$-tensor theory. The first scheme is based on using a truncation procedure of the energy, which allows for an unconditionally energy stable first order accurate decoupled scheme. The second scheme uses a modified second order accurate optimal dissipation algorithm, which gives a second order accurate coupled scheme. Finally, the third scheme uses a new idea to decouple the unknowns from the second scheme which allows us to obtain accurate dynamics while improving computational efficiency. We present several numerical experiments to offer a comparative study of the accuracy, efficiency and the ability of the numerical schemes to represent realistic dynamics.

翻译：本文采用Landau-de Gennes $\textbf{Q}$-张量理论，提出了三种用于模拟向列型液晶的线性数值格式。第一种格式基于能量截断方法，实现了无条件能量稳定的一阶精度解耦格式。第二种格式采用修正的二阶最优耗散算法，构建了二阶精度耦合格式。最后，第三种格式利用新思路对第二种格式中的未知量进行解耦，在提高计算效率的同时保持了动力学模拟的准确性。我们通过若干数值实验，对这些格式在精度、效率及复现真实动力学行为方面的能力进行了比较研究。