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 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.

Computational results show a significant improvement of the solution, in particular for the pressure in the case of smooth domains.

}, author = {Bänsch, Eberhard}, doi = {10.1016/j.cma.2014.06.030}, faupublication = {yes}, journal = {Computer Methods in Applied Mechanics and Engineering}, keywords = {Navier–Stokes equations; Traction boundary condition; Open boundary condition; Pressure correction; Finite elements}, pages = {198-211}, peerreviewed = {Yes}, title = {{A} finite element pressure correction scheme for the {Navier}-{Stokes} equations with traction boundary condition}, volume = {279}, year = {2014} }