I am working on a CFD problem where there is a axisymetric jet impinging normally on a flat plate. In this problem the flow boundary conditions are not known away from the jet. I have been updating the velocity boundary conditions using the continuity equation and this works o.k. But my big problem is when I add the buoyancy term to the N-S equations I have alot of convergence problems. This is a steady state problem but this type of boundary condition makes the system of equations very sensitive to any added features to the flow field. Does anyone have any suggestions on how to improve the stability and convergence of this type of problem. Any comments would be greatly appreciated.

For a free boundary problem, you might try using what some call "exit" conditions where you specify that total fluid forces are equal to zero on the boundary. For compressible calculations, there are BC's defined by Thomson which specify that there is no reflection of characteristic variables on the boundary. I'm sorry but I don't have that reference close at hand.