# Domain decomposition methods for the coupling of surface and groundwater flows

## Dr. Marco Discacciati

**Dec. 20, 2004, 8:30 a.m. HF 136**

This presentation concerns the study of mathematical and numerical models for simulating incompressible fluid flows through heterogeneous media. In particular, we consider the case of free fluids which can filtrate through a porous medium oc-cupying a neighbouring domain to the fluid one. This topic has many important ap-plications, among which we recall the hydrological environmental ones and mass transfer in biomechanics. In this talk we outline the mathematical and numerical analysis of a coupled Navier-Stokes/Darcy problem. In particular, by adopting the Beavers and Joseph interface conditions, we will assess the well-posedness of the global problem, and we will introduce a suitable Galerkin finite element approxima-tion. Then, we will focus our attention on iterative substructuring methods inspired by domain decomposition theory which allows to solve the global problem through the independent solution of both the fluid and the porous media subproblems in each subdomain. Through the analysis of suitable Steklov-Poincar?e interface op-erators, we can characterize optimal preconditioners to solve the discrete algebraic problem, which can be applied in the framework of Krylov type methods. The effec-tiveness of the computational methods that we have introduced will be shown on some test cases, with particular concern on the dependence of these methods on the gris size and on the most relevant physical parameters which characterize the filtration problem.