The Coupling Navier-Stokes/Darcy Systems by Vorticity-Velocity-Pressure Formulation

In this paper We consider the Coupling Navier-Stokes/Darcy equations in a two or three dimensional domain provided with non standard boundary conditions which involve the normal component of the velocity and the tangential components of the vorticity. We establish a coupled variational formulation of this problem with three independent unknowns: the vorticity, the velocity and the pressure. 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. Keywords: coupled problem, Darcy's equation, Navier-Stokes equation, Finite element.