Einladung zu einem Vortrag von:
Marco Discacciati
EPFL - Swiss Federal Institute of Technology
Montag, 20. Dezember 2004
09:30 Uhr, HF 136
Domain decomposition methods for the coupling of surface and
groundwater flows
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.
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