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In this paper we propose a finite volume method to solve the coupled Stokes-Darcy problem using steady Stokes equations for the fluid region and Darcy equations for the porous region.
At the contact interface between the fluid region and the porous media we imposed two conditions. The first one is the normal continuity of the velocity, while the second one is the continuity of the pressure. Furthermore, due to the lack of information about both the velocity and the pressure on the interface, we will use schwarz domain decomposition method.
In Darcy equations, the tensor of permeability will be considered as variable, since it depends on both the prop- erties of the porous medium and the viscosity of the fluid. Numerical examples are presented to demonstrate the efficiency of the proposed method
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