Work

Length preserving numerical schemes for the nematic liquid crystal flows

Year: 2025

Type: article

Abstract: In this paper, we introduce two novel classes of length preserving schemes for the Ericksen– Leslie model based on two distinct Lagrange multiplier approaches. In the first approach, the Lagrange multiplier q ( x , t ) is defined as |∇ d | 2 at the continuous level. In the second approach, q ( x , t ) is introduced at the discrete level to enforce the length constraint, while it remains identically zero at the continuous level. Within a predictor-corrector framework, we develop efficient and robust second-order length preserving schemes for the Ericksen–Leslie model. A series of numerical experiments are presented to verify the accuracy, stability, and energy dissipation properties of the proposed schemes. In addition, numerical comparisons show that our schemes achieve significantly improved computational efficiency compared to the existing method.

Source: ESAIM Mathematical Modelling and Numerical Analysis

DOI: 10.1051/m2an/2025082

Authors: Ruonan Cao, Nianyu Yi

Institution: Xiangtan University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid:

Funder: National Natural Science Foundation of China