Slip with friction and penetration with resistance boundary conditions for the Navier–Stokes equations—numerical tests and aspects of the implementation

We consider slip with friction and penetration with resistance boundary conditions in the steady state Navier–Stokes equations. This paper describes some aspects of the implementation of these boundary conditions for finite element discretizations. Numerical tests on two- and three-dimensional channel flows across a step using the slip with friction boundary condition study the influence of the friction parameter on the position of the reattachment point and the reattachment line of the recirculating vortex, respectively.