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Analysis of the Stokes-Darcy problem with generalised interface conditions
journal contribution
posted on 2022-04-29, 14:09 authored by Elissa Eggenweiler, Marco DiscacciatiMarco Discacciati, Iryna RybakFluid flows in coupled systems consisting of a free-flow region and the adjacent porous medium appear in a variety of environmental settings and industrial applications. In many appli- cations, fluid flow is non-parallel to the fluid–porous interface that requires a generalisation of the Beavers–Joseph coupling condition typically used for the Stokes–Darcy problem. Generalised coupling conditions valid for arbitrary flow directions to the interface are recently derived using the theory of homogenisation and boundary layers. The aim of this work is the mathematical analysis of the Stokes– Darcy problem with these generalised interface conditions. We prove the existence and uniqueness of the weak solution of the coupled problem. The well-posedness is guaranteed under a suitable relation- ship between the permeability and the boundary layer constants containing geometrical information about the porous medium and the interface. We study the validity of the obtained results for realistic problems numerically and provide a benchmark for numerical solution of the Stokes–Darcy problem with generalised interface conditions.
Funding
Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project Number 327154368 – SFB 1313
History
School
- Science
Department
- Mathematical Sciences
Published in
ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN)Volume
56Issue
2Pages
727-742Publisher
EDP SciencesVersion
- VoR (Version of Record)
Rights holder
© The AuthorsPublisher statement
This is an Open Access Article. It is published by EDP Sciences under the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Full details of this licence are available at: https://creativecommons.org/licenses/by/4.0/Acceptance date
2022-03-02Publication date
2022-04-13Copyright date
2022ISSN
2822-7840eISSN
2804-7214Publisher version
Language
- en
Depositor
Dr Marco Discacciati. Deposit date: 3 March 2022Usage metrics
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