Energy Stable and Maximum Bound Principle Preserving Schemes for the [math]-Tensor Flow of Liquid Crystals

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2025-04-18 DOI:10.1137/23m1598866

Dianming Hou, Xiaoli Li, Zhonghua Qiao, Nan Zheng

{"title":"Energy Stable and Maximum Bound Principle Preserving Schemes for the [math]-Tensor Flow of Liquid Crystals","authors":"Dianming Hou, Xiaoli Li, Zhonghua Qiao, Nan Zheng","doi":"10.1137/23m1598866","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 2, Page 854-880, April 2025. <br/> Abstract. In this paper, we propose two efficient fully discrete schemes for [math]-tensor flow of liquid crystals by using the first- and second-order stabilized exponential scalar auxiliary variable (sESAV) approach in time and the finite difference method for spatial discretization. The modified discrete energy dissipation laws are unconditionally satisfied for both two constructed schemes. A particular feature is that, for two-dimensional (2D) and a kind of three-dimensional (3D) [math]-tensor flow, the unconditional maximum bound principle (MBP) preservation of the constructed first-order scheme is successfully established, and the proposed second-order scheme preserves the discrete MBP property with a mild restriction on the time-step sizes. Furthermore, we rigorously derive the corresponding error estimates for the fully discrete second-order schemes by using the built-in stability results. Finally, various numerical examples validating the theoretical results, such as the orientation of liquid crystal in 2D and 3D, are presented for the constructed schemes.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"17 1","pages":""},"PeriodicalIF":2.8000,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Numerical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1598866","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

Abstract

SIAM Journal on Numerical Analysis, Volume 63, Issue 2, Page 854-880, April 2025.
Abstract. In this paper, we propose two efficient fully discrete schemes for [math]-tensor flow of liquid crystals by using the first- and second-order stabilized exponential scalar auxiliary variable (sESAV) approach in time and the finite difference method for spatial discretization. The modified discrete energy dissipation laws are unconditionally satisfied for both two constructed schemes. A particular feature is that, for two-dimensional (2D) and a kind of three-dimensional (3D) [math]-tensor flow, the unconditional maximum bound principle (MBP) preservation of the constructed first-order scheme is successfully established, and the proposed second-order scheme preserves the discrete MBP property with a mild restriction on the time-step sizes. Furthermore, we rigorously derive the corresponding error estimates for the fully discrete second-order schemes by using the built-in stability results. Finally, various numerical examples validating the theoretical results, such as the orientation of liquid crystal in 2D and 3D, are presented for the constructed schemes.

查看原文本刊更多论文

液晶[数学]张量流的能量稳定和最大界原理保持方案

SIAM数值分析杂志，第63卷，第2期，第854-880页，2025年4月。摘要。本文采用一阶和二阶稳定指数标量辅助变量法（sESAV）和有限差分法（spatial discretization）对液晶的[math]张量流动进行了两种有效的完全离散。两种构造格式均无条件满足修正后的离散能量耗散规律。一个特别的特点是，对于二维（2D）和一类三维（3D） [math]张量流，成功地建立了所构造的一阶格式的无条件最大界原理（MBP）保存，所提出的二阶格式保留了离散的MBP性质，对时间步长有轻微的限制。此外，利用内建的稳定性结果，我们严格地推导了完全离散二阶格式的相应误差估计。最后，对所构建的方案进行了二维和三维液晶取向等数值计算，验证了理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.