Yuksel, C. and Lesnic, D. orcid.org/0000-0003-3025-2770 (2024) The identification of obstacles immersed in a steady incompressible viscous fluid. Journal of Engineering Mathematics, 144 (1). 16. ISSN 0022-0833
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This is an author produced version of an article accepted for publication in the Journal of Engineering Mathematics, made available under the terms of the Creative Commons Attribution License (CC-BY), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. |
Keywords: | Finite element method; Fluid flows; Inverse geometry problems; Navier–Stokes equations |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 03 Jan 2024 10:36 |
Last Modified: | 07 Feb 2024 16:13 |
Status: | Published |
Publisher: | Springer Nature |
Identification Number: | 10.1007/s10665-023-10323-1 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:206953 |