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Numerical analysis of the Navier-Stokes/Darcy coupling
We consider a differential system based on the coupling of the Navier– Stokes and Darcy equations for modeling the interaction between surface and porous-media flows. We formulate the problem as an interface equation, we analyze the associated (nonlinear) Steklov–Poincaré operators, and we prove its well-posedness. We propose and analyze iterative methods to solve a conforming finite element approximation of the coupled problem.
The first author acknowledges the financial support from the program SCOPES n. IB7320–110721 and from IACS, EPFL. The other authors acknowledge the support of the FNS Project n. 200020–117587 “Interface operators and solutions algorithms for fluid–structure interaction problems with applications”. The second author acknowledges also the Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria, for partially supporting this research. Finally, the third author acknowledges also the financial support from the program Cofin MIUR PRIN 2007 n. 200774A7LH_001 “Mathematical and numerical modelling for cardiovascular and fluid dynamics applications”.
- Mathematical Sciences