A Finite Element Approximation for Nematic Liquid Crystal Flow with Stretching Effect Based on Nonincremental Pressure-Correction Method
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 noni...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/24/12/1844 |
| _version_ | 1827639788849594368 |
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| author | Zhaoxia Meng Meng Liu Hongen Jia |
| author_facet | Zhaoxia Meng Meng Liu Hongen Jia |
| author_sort | Zhaoxia Meng |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T16:47:59Z |
| format | Article |
| id | doaj.art-858bcadcc6464482b4a724a8bc4b2421 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T16:47:59Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-858bcadcc6464482b4a724a8bc4b24212023-11-24T14:44:02ZengMDPI AGEntropy1099-43002022-12-012412184410.3390/e24121844A Finite Element Approximation for Nematic Liquid Crystal Flow with Stretching Effect Based on Nonincremental Pressure-Correction MethodZhaoxia Meng0Meng Liu1Hongen Jia2Department of Energy and Power Engineering, Shanxi Energy Institute, Taiyuan 030024, ChinaSchool of Mathematics, Taiyuan University of Technology, Taiyuan 030024, ChinaSchool of Mathematics, Taiyuan University of Technology, Taiyuan 030024, ChinaIn 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.https://www.mdpi.com/1099-4300/24/12/1844nematic liquid crystalfinite elementsnonincremental pressure-correction projection methoddecoupled numerical scheme |
| spellingShingle | Zhaoxia Meng Meng Liu Hongen Jia A Finite Element Approximation for Nematic Liquid Crystal Flow with Stretching Effect Based on Nonincremental Pressure-Correction Method Entropy nematic liquid crystal finite elements nonincremental pressure-correction projection method decoupled numerical scheme |
| title | A Finite Element Approximation for Nematic Liquid Crystal Flow with Stretching Effect Based on Nonincremental Pressure-Correction Method |
| title_full | A Finite Element Approximation for Nematic Liquid Crystal Flow with Stretching Effect Based on Nonincremental Pressure-Correction Method |
| title_fullStr | A Finite Element Approximation for Nematic Liquid Crystal Flow with Stretching Effect Based on Nonincremental Pressure-Correction Method |
| title_full_unstemmed | A Finite Element Approximation for Nematic Liquid Crystal Flow with Stretching Effect Based on Nonincremental Pressure-Correction Method |
| title_short | A Finite Element Approximation for Nematic Liquid Crystal Flow with Stretching Effect Based on Nonincremental Pressure-Correction Method |
| title_sort | finite element approximation for nematic liquid crystal flow with stretching effect based on nonincremental pressure correction method |
| topic | nematic liquid crystal finite elements nonincremental pressure-correction projection method decoupled numerical scheme |
| url | https://www.mdpi.com/1099-4300/24/12/1844 |
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