The identification of obstacles immersed in a steady incompressible viscous fluid

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
G. Yuksel, D. Lesnic
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Abstract

In this paper, the identification of immersed obstacles in a steady incompressible Navier–Stokes viscous fluid flow from fluid traction measurements is investigated. The solution of the direct problem is computed using the finite element method (FEM) implemented in the Freefem++ commercial software package. The solution of the inverse geometric obstacle problem (parameterized by a small set of unknown constants) is accomplished iteratively by minimizing the nonlinear least-squares functional using an adaptive moment estimation algorithm. The numerical results for the identification of an obstacle in a viscous fluid flowing in a channel with open ends, show that when the fluid traction is measured on the top, bottom and inlet boundaries, then the algorithm provides accurate and robust reconstructions of an obstacle parameterized by a small number of parameters in a Fourier trigonometric finite expansion. Stable reconstructions with respect to noise in the measured fluid traction data are also achieved, although for complicated shapes parameterized by larger degrees of freedom Tikhonov regularization of the least-squares functional may need to be employed. Multiple-component obstacles may also be identified provided that a good initial guess is provided. In case of limited data being available only at the inlet boundary the pressure gradient provides more information for inversion than the fluid traction.

Abstract Image

沉浸在稳定的不可压缩粘性流体中的障碍物的识别
本文研究了根据流体牵引测量结果识别稳定不可压缩纳维-斯托克斯粘性流体流动中的沉浸障碍物。直接问题的解是用 Freefem++ 商业软件包中的有限元法(FEM)计算的。通过使用自适应矩估计算法最小化非线性最小二乘法函数,反复求解反几何障碍问题(由一小组未知常数参数化)。对在两端开口的通道中流动的粘性流体中的障碍物进行识别的数值结果表明,当在顶部、底部和入口边界测量流体牵引力时,该算法可通过傅里叶三角有限展开中的少量参数对障碍物进行精确、稳健的重构。虽然对于参数自由度较大的复杂形状,可能需要对最小二乘法函数进行提霍诺夫正则化处理,但该算法也能实现与测量流体牵引数据中的噪声有关的稳定重构。只要有一个良好的初始猜测,多分量障碍物也可以被识别出来。如果只有入口边界的有限数据,压力梯度比流体牵引力能提供更多反演信息。
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
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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