The interface control domain decomposition method for Stokes-Darcy coupling (Q2798656)

The coupling between Stokes and Darcy equations is solved by the Interface Control Domain Decomposition (ICDD) method. Because the ICDD method introduces new auxiliary control variables on the subdomain interfaces as unknown fluxes of the state solutions of the subproblems, a PDE constrained optimal control problem on the overlapping subdomains has to be solved. The controls and observation are defined on the interfaces. The authors analyze the ICDD method for the Stokes-Darcy coupling with Dirichlet type controls, where the cost functional measures the gap between Stokes and Darcy velocities on one interface and the gap in the pressures on the other one. In this way, the Stokes and Darcy subproblems are closed by the Dirichlet boundary conditions on the interfaces, therefore fluxes or tangential derivatives, or auxiliary problems inside the overlapping region, are not evaluated. Numerical results show that the ICDD method provides accurate solutions on sharp interfaces for near parallel and near normal flows to the porous media compared with the approach using the Beavers-Joseph-Saffman (BJS) condition.The ICDD method requires less memory than the Sharp Interface- (SI)-BJS approach. The computational cost per iteration step for the ICDD method is a little higher than for the SI-BJS method.