Application of defined auxiliary system in the method of layer potentials for solving the stokes flow problem

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Engineering Analysis with Boundary Elements Pub Date : 2025-01-13 DOI:10.1016/j.enganabound.2024.106102

Kue-Hong Chen , Yi-Kui Liu , Jeng-Tzong Chen

引用次数: 0

Abstract

In this article, we apply an error estimation technique to assess the numerical error of seven kinds of method of layer potentials for solving the Stokes flow problem governed by the biharmonic equation. The new error estimation technique allows us to estimate numerical errors in situations where analytical solutions are not available. Additionally, it enables us to determine the optimal solution for the seven methods, making them applicable in various engineering problems. We validate the developed algorithm through four numerical experiments on 2D flows: (1) a gear cavity, (2) a circular cavity, (3) a lid-driven square cavity, and (4) an amoeba-shaped cavity. The results demonstrate close agreement with previous research, affirming that the error estimation technique can guarantee the method of layer potentials an accurate and versatile approach to solving the Stokes flow problem.

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层势法中定义辅助系统在求解斯托克斯流问题中的应用

本文应用误差估计技术对求解双调和方程下Stokes流问题的7种层势法的数值误差进行了估计。新的误差估计技术使我们能够在无法得到解析解的情况下估计数值误差。此外，它使我们能够确定这七种方法的最优解，使它们适用于各种工程问题。我们通过四个二维流动的数值实验来验证所开发的算法：(1)齿轮腔，(2)圆形腔，(3)盖驱动的方形腔和(4)变形虫形腔。结果与前人的研究结果一致，证实了误差估计技术可以保证层势法是求解Stokes流问题的一种准确、通用的方法。

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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来源期刊

Engineering Analysis with Boundary Elements 工程技术-工程：综合

CiteScore

5.50

自引率

18.20%

发文量

368

审稿时长

56 days

期刊介绍： This journal is specifically dedicated to the dissemination of the latest developments of new engineering analysis techniques using boundary elements and other mesh reduction methods. Boundary element (BEM) and mesh reduction methods (MRM) are very active areas of research with the techniques being applied to solve increasingly complex problems. The journal stresses the importance of these applications as well as their computational aspects, reliability and robustness. The main criteria for publication will be the originality of the work being reported, its potential usefulness and applications of the methods to new fields. In addition to regular issues, the journal publishes a series of special issues dealing with specific areas of current research. The journal has, for many years, provided a channel of communication between academics and industrial researchers working in mesh reduction methods Fields Covered: • Boundary Element Methods (BEM) • Mesh Reduction Methods (MRM) • Meshless Methods • Integral Equations • Applications of BEM/MRM in Engineering • Numerical Methods related to BEM/MRM • Computational Techniques • Combination of Different Methods • Advanced Formulations.