Navier-Stokes方程的变时间步长IMEX-BDF2 SAV格式及其尖锐误差估计

IF 1.9 3区数学 Q2 Mathematics

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2023-01-24 DOI:10.1051/m2an/2023007

Yana Di, Yuheng Ma, Jie Shen, Jiwei Zhang

{"title":"Navier-Stokes方程的变时间步长IMEX-BDF2 SAV格式及其尖锐误差估计","authors":"Yana Di, Yuheng Ma, Jie Shen, Jiwei Zhang","doi":"10.1051/m2an/2023007","DOIUrl":null,"url":null,"abstract":"We generalize the implicit-explicit (IMEX) second-order backward difference (BDF2) scalar auxil- iary variable (SAV) scheme for Navier-Stokes equation with periodic boundary conditions [11, Huang and Shen, SIAM J. Numer. Anal., 2021] to a variable time-step IMEX-BDF2 SAV scheme, and carry out a rigorous stability and convergence analysis. The key ingredients of our analysis are a new modified discrete Grönwall inequality, exploration of the discrete orthogonal convolution (DOC) kernels, and the unconditional stability of the proposed scheme. We derive global and local optimal H 1 error estimates in 2D and 3D, respectively. Our analysis provides a theoretical support for solv- ing Navier-Stokes equations using variable time-step IMEX-BDF2 SAV schemes. We also design an adaptive time-stepping strategy, and provide ample numerical examples to confirm the effectiveness and eﬀiciency of our proposed methods.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2023-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A variable time-step IMEX-BDF2 SAV scheme and its sharp error estimate for the Navier-Stokes equations\",\"authors\":\"Yana Di, Yuheng Ma, Jie Shen, Jiwei Zhang\",\"doi\":\"10.1051/m2an/2023007\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We generalize the implicit-explicit (IMEX) second-order backward difference (BDF2) scalar auxil- iary variable (SAV) scheme for Navier-Stokes equation with periodic boundary conditions [11, Huang and Shen, SIAM J. Numer. Anal., 2021] to a variable time-step IMEX-BDF2 SAV scheme, and carry out a rigorous stability and convergence analysis. The key ingredients of our analysis are a new modified discrete Grönwall inequality, exploration of the discrete orthogonal convolution (DOC) kernels, and the unconditional stability of the proposed scheme. We derive global and local optimal H 1 error estimates in 2D and 3D, respectively. Our analysis provides a theoretical support for solv- ing Navier-Stokes equations using variable time-step IMEX-BDF2 SAV schemes. We also design an adaptive time-stepping strategy, and provide ample numerical examples to confirm the effectiveness and eﬀiciency of our proposed methods.\",\"PeriodicalId\":50499,\"journal\":{\"name\":\"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2023-01-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1051/m2an/2023007\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1051/m2an/2023007","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 0

摘要

本文推广了具有周期边界条件的Navier-Stokes方程的隐显(IMEX)二阶后向差分(BDF2)标量辅助变量(SAV)格式[11]。分析的[j]， 2021]对变时间步长IMEX-BDF2 SAV方案进行了研究，并进行了严格的稳定性和收敛性分析。我们分析的关键成分是一个新的修正的离散Grönwall不等式，探索离散正交卷积(DOC)核，以及所提方案的无条件稳定性。我们分别导出了二维和三维的全局和局部最优h1误差估计。本文的分析为利用变时间步长IMEX-BDF2 SAV格式求解Navier-Stokes方程提供了理论支持。我们还设计了一种自适应时步策略，并提供了大量的数值实例来验证我们所提出方法的有效性和效率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A variable time-step IMEX-BDF2 SAV scheme and its sharp error estimate for the Navier-Stokes equations

We generalize the implicit-explicit (IMEX) second-order backward difference (BDF2) scalar auxil- iary variable (SAV) scheme for Navier-Stokes equation with periodic boundary conditions [11, Huang and Shen, SIAM J. Numer. Anal., 2021] to a variable time-step IMEX-BDF2 SAV scheme, and carry out a rigorous stability and convergence analysis. The key ingredients of our analysis are a new modified discrete Grönwall inequality, exploration of the discrete orthogonal convolution (DOC) kernels, and the unconditional stability of the proposed scheme. We derive global and local optimal H 1 error estimates in 2D and 3D, respectively. Our analysis provides a theoretical support for solv- ing Navier-Stokes equations using variable time-step IMEX-BDF2 SAV schemes. We also design an adaptive time-stepping strategy, and provide ample numerical examples to confirm the effectiveness and eﬀiciency of our proposed methods.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique 数学-应用数学

CiteScore

2.70

自引率

5.30%

发文量

审稿时长

6-12 weeks

期刊介绍： M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.