The Coupling Navier-Stokes/Darcy Systems by Vorticity-Velocity-Pressure Formulation - Younes, Anis; Ouali, Yousra (Global Journal of Mathematical Analysis, 2014)
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.