A finite element pressure correction scheme for the Navier–Stokes equations with traction boundary condition

We consider the popular pressure correction scheme for the solution of the time dependent Navier–Stokes equations with traction boundary condition. A finite element based method to improve the performance of the classical approach is proposed. The improvement is achieved by modifying the traction boundary condition for the provisional velocity u ̃ n + 1 in each time step. The corresponding term consists of a simple boundary functional involving the normal derivative of the pressure correction that can be evaluated in a natural and easy way in the context of finite elements. ational results show a significant improvement of the solution, in particular for the pressure in the case of smooth domains.