Full paper in PDF format:
$%M. Discacciati and A. Quarteroni, Navier-Stokes/Darcy Coupling: Modeling, analysis, and numerical approximation, Rev. Mat. Complut. 22 (2009), no. 2, 315–426.%$
Navier-Stokes/Darcy Coupling: Modeling, Analysis, and Numerical Approximation
Marco DISCACCIATI 1,  and Alfio QUARTERONI 1,2,
1IACS - Chair of Modeling and Scientific Computing
Ecole Polytechnique Fédérale de Lausanne
CH-1015 Lausanne — Switzerland
alfio.quarteroni@epfl.ch
2MOX, Politecnico di Milano
P.zza Leonardo da Vinci 32
I-20133 Milano — Italy
marco.discacciati@epfl.ch
Received: November 21, 2008
Accepted
: April 16, 2009

ABSTRACT

This paper is an overview of known and new results about the coupling of Navier-Stokes and Darcy equations to model the filtration of incompressible fluids through porous media. We discuss coupling conditions and we analyze the global coupled model in order to prove its well-posedness and to characterize effective algorithms to compute the solution of its numerical approximation.

Key words: Navier-Stokes equations, Darcy’s law, Interface conditions, Domain decomposition, Finite elements, Environmental flows, Blood flow.

2000 Mathematics Subject Classification: 76D05, 76S05, 65M60, 65M55, 86A05, 76Z05.