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
Yana Di, Yuheng Ma, Jie Shen, Jiwei Zhang
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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。
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.
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来源期刊
CiteScore
2.70
自引率
5.30%
发文量
27
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.
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