Boundary conditions on artificial frontiers for incompressible and compressible Navier-Stokes equations

Non reflecting boundary conditions on artificial frontiers of the domain are proposed for both incompressible and compressible Navier-Stokes equations. For incompressible flows, the boundary conditions lead to a well-posed problem, convey properly the vortices without any reflections on the artificial limits and allow to compute turbulent flows at high Reynolds numbers. For compressible hows, the boundary conditions convey properly the vortices without any reflections on the artificial limits and also avoid acoustic waves that go back into the flow and change its behaviour. Numerical tests illustrate the efficiency of the various boundary conditions.