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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.17289 |
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| _version_ | 1866929288632074240 |
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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 |