PEGASE: A Navier-Stokes solver for direct numerical simulation of incompressible flows The authors propose a hybrid conservative finite difference/finite element scheme for the solution of the unsteady incompressible Navier-Stokes equation. Using velocity-pressure variables on a non-staggered grid, the solution is obtained with a projection method based on the resolution of a pressure Poisson equation. Two- and three-dimensional unsteady separated flows with open boundaries have been simulated with the proposed method. The effectiveness of this approach is illustrated on numerical examples.