A Finite Element Approximation for Nematic Liquid Crystal Flow with Stretching Effect Based on Nonincremental Pressure-Correction Method

Zhaoxia Meng; Meng Liu; Hongen Jia

doi:10.3390/e24121844

A Finite Element Approximation for Nematic Liquid Crystal Flow with Stretching Effect Based on Nonincremental Pressure-Correction Method

Entropy (Basel). 2022 Dec 18;24(12):1844. doi: 10.3390/e24121844.

Authors

Zhaoxia Meng¹, Meng Liu², Hongen Jia²

Affiliations

¹ Department of Energy and Power Engineering, Shanxi Energy Institute, Taiyuan 030024, China.
² School of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China.

Abstract

In this paper, a new decoupling method is proposed to solve a nematic liquid crystal flow with stretching effect. In the finite element discrete framework, the director vector is calculated by introducing a new auxiliary variable w, and the velocity vector and scalar pressure are decoupled by a nonincremental pressure-correction projection method. Then, the energy dissipation law and unconditional energy stability of the resulting system are given. Finally, some numerical examples are given to verify the effects of various parameters on the singularity annihilation, stability and accuracy in space and time.

Keywords: decoupled numerical scheme; finite elements; nematic liquid crystal; nonincremental pressure-correction projection method.

Grants and funding

The research was funded by the 2021 Shanxi Science and Technology Cooperation and Exchange special program “202104041101019”, the 2022 Shanxi Water Conservancy Science and Technology Research and Promotion Project “2022GM006”.