Karageorghis, A. and Lesnic, D. orcid.org/0000-0003-3025-2770 (2024) Solution of the Cauchy problem for the Brinkman equations using an alternating method of fundamental solutions. Numerical Algorithms. ISSN 1017-1398
Abstract
In this paper, we intend to formulate and solve Cauchy problems for the Brinkman equations governing the flow of fluids in porous media, which have never been investigated before in such an inverse formulation. The physical scenario corresponds to situations where part of the boundary of the fluid domain is hostile or inaccessible, whilst on the remaining friendly part of the boundary we prescribe or measure both the fluid velocity and traction. The resulting mathematical formulation leads to a linear but ill-posed problem. A convergent algorithm based on solving two sub-sequences of mixed direct problems is developed. The direct solver is based on the method of fundamental solutions which is a meshless boundary collocation method. Since the investigated problem is ill-posed, the iterative process is stopped according to the discrepancy principle at a threshold given by the amount of noise with which the input measured data is contaminated in order to prevent the manifestation of instability. Results inverting both exact and noisy data for two- and three-dimensional problems demonstrate the convergence and stability of the proposed numerical algorithm.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use (https://www.springernature.com/gp/open-research/policies/accepted-manuscript-terms), but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s11075-024-01837-5 |
Keywords: | Cauchy problem; Inverse problem; Brinkman flow; Method of fundamental solutions |
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: | 08 Apr 2024 09:38 |
Last Modified: | 03 May 2024 11:13 |
Published Version: | 10.1007/s11075-024-01837-5 |
Status: | Published online |
Publisher: | Springer |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:211242 |
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Filename: Andreas Karageorghis and Daniel Lesnic 2024.pdf
