Interface Control Domain Decomposition (ICDD) Method for Stokes-Darcy coupling
Tuesday 6th May 2014
Discacciati, M.; Gervasio, P.; Quarteroni, A.
We propose the ICDD method 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, an efficient solution algorithm is proposed, and several numerical tests are implemented. Our results show the accuracy of the ICDD methos, 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 is more versatile and easier to implement than the model based on the Beavers, Joseph and Saffman coupling conditions.