I am using SIMPLE algorithm on unstructured mesh and I am using collocated variables.

On the ourflow boundary, I tried a non-reflecting boundary condition. I set du/dn=0 and dv/dn=0 and dp'/dn=const. The out normal direction is the same as u component velocity. p' is the pressure correction. It never worked for me. I change the boundary condition of p' to p'=0, but it doesn't work either.

I have to set the normal velocity and no its gradient. I don't know for imcompressible flow, whether I can set a zero gradient boundary condition for velocity.

Yes. The zero gradient BC for u, v is OK. dp'/dn=0 does not work. In all the BCs, set p'=0.

Jack

I think what u want to do is set p'=0 on one edge, such as outlet, that is enough. ur problemm is ur code i think, i have writen a code and use SIMPLE successfuly to simulation packed column multiple flow . do check ur code to see if u miss something (Pataker's book)