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A second-order BDF convex splitting numerical scheme for the Ericksen-Leslie equation

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Abstract

In this paper, we develop a second-order backward differentiation formula (BDF) numerical scheme for the Ericksen-Leslie model of nematic liquid crystal. It combines a convex splitting method to discretize the penalty function. In the meanwhile, a pressure-correction strategy is used to decouple the pressure from that of the velocity. We prove that the proposed scheme is uniquely solvable and unconditionally stable in energy. Some numerical simulations are also performed to demonstrate the efficiency and accuracy of the proposed scheme.

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Data Availability

The data sets generated during and analyzed during the current study are available from the corresponding author on reasonable request.

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Funding

This work was supported by the Research Project Supported by Shanxi Scholarship Council of China (No.2021-029) and International Cooperation Base and platform project of Shanxi Province (No.202104041101019). Shanxi Province Natural Science Foundation (No.202203021211129).

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Authors and Affiliations

  1. College of Mathematics, Taiyuan University of Technology, Yuci, Jinzhong, 030600, Shanxi, China

    Ni Miao, Haifeng Zhang & Jing Liu

  2. College of Mathematics, Taiyuan University of Technology, Wanbolin, Taiyuan, 030024, Shanxi, China

    Danxia Wang

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  1. Ni Miao
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  2. Danxia Wang
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  3. Haifeng Zhang
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  4. Jing Liu
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Correspondence to Danxia Wang.

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Miao, N., Wang, D., Zhang, H. et al. A second-order BDF convex splitting numerical scheme for the Ericksen-Leslie equation. Numer Algor 94, 293–314 (2023). https://doi.org/10.1007/s11075-023-01501-4

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  • DOI: https://doi.org/10.1007/s11075-023-01501-4

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