Mathematical and numerical models for coupling surface and groundwater flows

Authors:
Marco Discacciati;Edie Miglio;Alfio Quarteroni
Affiliations:
Politecnico di Milano, Dipartimento di Matematica "F. Brioschi", Piazza Leonardo da Vinci 32, 20133 Milano, Italy;Département de Mathématiques, École Polytecnique Fédérale de Lausanne, CH-1015, Lausanne, Switzerland;Politecnico di Milano, Dipartimento di Matematica "F. Brioschi", Piazza Leonardo da Vinci 32, 20133 Milano, Italy and Département de Mathématiques, École Polytecnique Fédé ...
Venue:
Applied Numerical Mathematics
Year:
2002

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Abstract

In this paper we present some results about the coupling of Navier-Stokes and Shallow Water equations for surface flows and Darcy's equation for groundwater flows. We discuss suitable interface conditions and show the well-posedness of the coupled problem in the case of a linear Stokes problem. An iterative method to compute the solution is proposed. At each step this method requires the solution of one problem in the fluid part and one in the porous medium. Finally we introduce the Steklov-Poincaré equation associated to the coupled problem.