I am trying to move my program from the cavity flow to flow between two plates using the stream function/vorticity equations, and I am having trouble with the exit. For the entrance I assumed a uniform flow field. This gave Uy=0 and Ux=const, which led to vorticity=0 at the entrance, which makes sense. For the exit, I am also getting zero if I assume fully developed flow. Is that correct?

thanks

Look at the definition of vorticity, consider a non-uniform (fully developed) velocity profile, and you will realize that vorticity cannot be zero in fully developed flow between two plates.

I know it is not zero between the plates. I am trying to get the BCs at the entrance and exit. I have the BCs for the top and bottom.

thanks for your help

Maybe I misunderstood your question. Just to make sure: The vorticity is not zero anywhere in a fully developed flow. This means that you cannot use zero vorticity at the exit boundary condition. If you know the velocity profile at the exit, you can then obtain the appropriate (non-zero) vorticity and apply that as a boundary condition. Does this answer your question?

thanks, that helps out. I am having most of my trouble at the exit. So, I can use the curl of the velocity vector to find the vorticity at the exit and set that as the boundary condition? I think I can make that work in my program.

thanks