The ADI (Alternating Direction Implicit) method is used for solving second order partial differential equations. In this case it is applied for viscid incompressible fluid flow described by the Navier-Stokes equation. The method is tested on the simple case of the abrupt area change for the several Reynolds numbers up to Re = 800. A vortex is formed already at low Reynolds number. It affects the pressure field and contribute to the phenomena complicity. The influence of the boundary conditions and nodalization density is also examined.