Abstract
A finite element method for the numerical solution of the anisotropic Navier-Stokes equations in shallow domain is presented. This method take into account aspect ratio in the hydrostatic approximation of the Navier-Stokes equations \cite{beslay,azthese,azgui}. A projection method \cite{guermond,shen} is used for the time discretization. The linear systems are solved via a some preconditioned conjugate algorithm, well adapted to massively parallel computers \cite{julien_these,julien_precond,julien_precond_paral}. Some results are presented for the wind driven water circulation in the North Atlantic.
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