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Mathematical and numerical models for coupling surface and groundwater flows. (English) Zbl 1023.76048
Summary: We present some results on coupling Navier-Stokes with shallow water equations for surface flows, and with 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 is proposed to compute the solution. At each step this method requires the solution of one problem in the fluid part and one in the porous medium. Finally, we introduce Steklov-Poincaré equation associated with the coupled problem.

MSC:
76S05 Flows in porous media; filtration; seepage
76D05 Navier-Stokes equations for incompressible viscous fluids
35Q35 PDEs in connection with fluid mechanics
86A05 Hydrology, hydrography, oceanography
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