When using the pressure projection method to solve the incompressible Navier-Stokes equations do we apply Neumann boundary conditions for pressure only where there are associated no-slip velocity boundary conditions? For example suppose we were trying to solve the vortex shedding problem. The velocity boundary conditions are shown in the figure
Then would I use a Neumann condition on pressure for the top, bottom, and circle? If so what about the left and right sides where the velocity is not no-slip? Would I have to specify a Dirichlet pressure here and if so then what would that be? I know that in order to solve the Poisson type problem for pressure that at least one node (I am using finite elements) must be specified in order for the system to have a unique solution, but should we be specifying pressure at all nodes where there is not a no-slip boundary condition on velocity? The related question Flow past a cylinder - Projection Method - Boundary Conditions seemed to indicate that Neumann conditions on pressure are only used when that boundary also has a no-slip velocity boundary condition. Is this correct?