Boundary conditions for a divergence free velocity–pressure formulation of the Navier–Stokes equations

New sets of boundary conditions for the velocity–pressure formulation of the incompressible Navier–Stokes equations are derived. The boundary conditions have the same form on both inflow and outflow boundaries and lead to a divergence free solution. Moreover, the specific form of the boundary condition makes it possible derive a symmetric positive definite equation system for the internal pressure. Numerical experiments support the theoretical conclusions.