BC's for stream function equation...
 

Sir,

I am using stream-function vorticity formulation for flow over a flat plate problem. I am solving these steady state equations by line-by-line algorithm. for that far away from the plate I have to use a mixed derivative boundary condition ie (mixed derivative of psi wrt both x and y =0) for stream function equation. But in this case i am not able to tackle this bc using fictitious point method. Please help me if anybody know how to apply this bc...

you can try v=0 and u=U at that boundary..U is the freestream velocity. Sort of like a symmetry line, but is actually a moving wall ( Fromm 1963 and Fromm and Harlow 1963)

Thank you for ur reply
But my actual problem is mixed convection heat transfer. So it should give results for both natural and forced convection regimes. For natural convection u and v are zeros. Only possible bc is d^2(psi)/dxdy=0. But I cant apply this Bc directly to discretized stream-function equation.

how are you getting u and v to be zero?

For natural convection occurs due to density change(buoyancy) caused by temperature gradient. therefore far away from the plate this effect is negligible fluid will be at rest both u and v will be zero...

if you are far enough from the plate free convection should be zero, as you stated and the BC should be driven by the forced convection flow, right? Have you tried to get the flow profile neglecting any free convection?