不可压缩流的pod - rom，包括全阶解的时间导数的快照:压力的错误界限

IF 3.8 2区数学 Q1 MATHEMATICS

Journal of Numerical Mathematics Pub Date : 2023-04-17 DOI:10.48550/arXiv.2304.08313

B. García-Archilla, V. John, Sarah Katz, J. Novo

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引用次数: 1

摘要

摘要研究了基于适当正交分解(POD)的不可压缩Navier-Stokes方程的降阶方法(ROMs)，该方法包含接近全阶混合有限元法(FOM)速度时间导数的快照。此外，这组快照包含了FOM的平均速度。FOM和po - rom都配备了梯度稳定。对这种方法的速度误差分析可以在文献中找到。本文研究了两种不同的压力近似计算方法，并证明了压力的误差范围与粘度的反幂无关。数值研究支持了分析结果，并对两种方法进行了比较。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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POD-ROMs for incompressible flows including snapshots of the temporal derivative of the full order solution: Error bounds for the pressure

Abstract Reduced order methods (ROMs) for the incompressible Navier–Stokes equations, based on proper orthogonal decomposition (POD), are studied that include snapshots which approach the temporal derivative of the velocity from a full order mixed finite element method (FOM). In addition, the set of snapshots contains the mean velocity of the FOM. Both the FOM and the POD-ROM are equipped with a grad-div stabilization. A velocity error analysis for this method can be found already in the literature. The present paper studies two different procedures to compute approximations to the pressure and proves error bounds for the pressure that are independent of inverse powers of the viscosity. Numerical studies support the analytic results and compare both methods.

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来源期刊

Journal of Numerical Mathematics 数学-数学

CiteScore

5.90

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Numerical Mathematics (formerly East-West Journal of Numerical Mathematics) contains high-quality papers featuring contemporary research in all areas of Numerical Mathematics. This includes the development, analysis, and implementation of new and innovative methods in Numerical Linear Algebra, Numerical Analysis, Optimal Control/Optimization, and Scientific Computing. The journal will also publish applications-oriented papers with significant mathematical content in computational fluid dynamics and other areas of computational engineering, finance, and life sciences.