Effective downstream boundary conditions for incompressible Navier–Stokes equations

The aim of this paper is to give open boundary conditions for the incompressible Navier–Stokes equations. From a weak formulation in velocity–pressure variables, some natural boundary conditions involving the traction or pseudotraction and inertial terms are established. Numerical experiments on the flow behind a cylinder show the efficiency of these conditions, which convey properly the vortices downstream. Comparisons with other boundary conditions for the velocity and pressure are also performed.