向列相液晶流的一种二阶全离散格式

A Second-Order Fully Discrete Scheme for Nematic Liquid Crystal Flow

在本文中,我们对向列相液晶流的Ginzburg-Landau模型提出了一种二阶、线性、耦合的格式,证明了该格式在离散条件下的能量稳定性,最后,通过数值模拟展示了四奇异点和旋转流的湮没过程,并且验证了格式的数值精度。结果表明:该格式具有能量稳定性,且具有比较好的数值精度。

In this paper, we mainly propose and analyze a second-order, linear, coupled scheme for the Ginzburg-Landau model of the nematic liquid crystal flow, and prove its energy stability under discrete condition. Finally, we demonstrate the annihilation process of four singularities and rotating flows through numerical simulations, and verify the numerical accuracy of the scheme. The results show that the scheme has energy stability and good numerical accuracy.