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Main Authors: Swain, Justin, Tierra, Giordano
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2403.17289
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author Swain, Justin
Tierra, Giordano
author_facet Swain, Justin
Tierra, Giordano
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2403_17289
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Linear Numerical Schemes for a $\textbf{Q}$-Tensor System for Nematic Liquid Crystals
Swain, Justin
Tierra, Giordano
Numerical Analysis
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.
title Linear Numerical Schemes for a $\textbf{Q}$-Tensor System for Nematic Liquid Crystals
topic Numerical Analysis
url https://arxiv.org/abs/2403.17289