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The interface control domain decomposition method for Stokes-Darcy coupling
journal contribution
posted on 2016-02-22, 10:46 authored by Marco DiscacciatiMarco Discacciati, Paola Gervasio, Alessandro Giacomini, Alfio QuarteroniThe ICDD method [15, 16] is here proposed to solve the coupling between Stokes and Darcy equations. According to this approach, the problem is formulated as an optimal control
problem whose control variables are the traces of the velocity and the pressure on the internal boundaries of the subdomains that provide an overlapping decomposition of the original computational domain. A theoretical analysis is carried out and the well-posedness of the problem is proved
under certain assumptions on both the geometry and the model parameters. An efficient solution algorithm is proposed, and several numerical tests are implemented. Our results show the accuracy of the ICDD method, its computational efficiency and robustness with respect to the different parameters involved (grid-size, polynomial degrees, permeability of the porous domain, thickness of the overlapping region). The ICDD approach turns out to be more versatile and easier to implement than the celebrated model based on the Beavers, Joseph and Saffman coupling conditions.
Funding
The first author acknowledges funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grand agreement no. 294229.
History
School
- Science
Department
- Mathematical Sciences
Published in
SIAM Journal on Numerical AnalysisVolume
54Issue
2Pages
1039 - 1068Citation
DISCACCIATI, M. ...et al., 2016. The interface control domain decomposition method for Stokes-Darcy coupling. SIAM Journal on Numerical Analysis, 54(2), pp.1039-1068.Publisher
© Society for Industrial and Applied MathematicsVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Acceptance date
2016-01-22Publication date
2016-04-12Notes
This paper was accepted for publication in the journal SIAM Journal on Numerical Analysis and the definitive published version is available at http://dx.doi.org/10.1137/15M101854XISSN
0036-1429eISSN
1095-7170Publisher version
Language
- en