We propose in this talk to study open boundary conditions for incompressible Navier-Stokes equations, in the framework of pressure- or/and velocity-correction methods. The standard way to enforce this type of boundary condition is described, followed by an adaptation of the one we proposed by Guermond et al that provides higher pressure and velocity convergence rate in space and time for pressure-correction schemes. Those two methods are illustrated with a numerical test with both a finite volume and a spectral element method. We conclude with two physical simulations: first, we study, in a geometry where a bifurcation takes place, the influence of Reynolds number on the laminar flow and secondly we verify the solution obtained for the unsteady flow around a square cylinder.