The interface control domain decomposition method for Stokes-Darcy coupling
journal contributionposted 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.
The first author acknowledges funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grand agreement no. 294229.
- Mathematical Sciences