DDFV method for Navier–Stokes problem with outflow boundary conditions

Abstract

We propose a Discrete Duality Finite Volume scheme (DDFV for short) for the unsteady incompressible Navier–Stokes problem with outflow boundary conditions. As in the continuous case, those conditions are derived from a weak formulation of the equations and they provide an energy estimate of the solution. We prove well-posedness of the scheme and a discrete energy estimate. Finally we perform some numerical tests simulating the flow behind a cylinder inside a long channel to show the robustness of such conditions in the DDFV framework.