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The interface control domain decomposition method for Stokes-Darcy coupling

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journal contribution
posted on 22.02.2016, 10:46 by Marco DiscacciatiMarco Discacciati, Paola Gervasio, Alessandro Giacomini, Alfio Quarteroni
The 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 Analysis

Volume

54

Issue

2

Pages

1039 - 1068

Citation

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 Mathematics

Version

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

22/01/2016

Publication date

2016-04-12

Notes

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/10.1137/15M101854X

ISSN

0036-1429

eISSN

1095-7170

Language

en