Different ans of poisson eqn with different solver

Quarkz

Hi,

I am trying to solve a simple laminar channel flow, uniform velocity in, supposedly parabolic profile out. hence, u=1 at west face inlet, no-slip at wall, convective BC at outlet.

since i'm using FVM fractional step, i need to solve a poisson eqn after the momentum eqn. however, i can't get a converged ans with iterative solve such as GMRES using NSPCG. When I used direct solver, such as IMSL library dlslrg (gaussian) or LAPACK 's dgesv (LU decomp), i get the same ans for both at the 1st step, but different ans after that. I'm wondering if there's something wrong with my BCs, which can be one of these:

1. dp/dx at all 4 sides, p=0 at outlet, others extrapolated 2. dp/dx at all 4 sides, p at edge face extrapolated 3. dp/dx at all except outlet, p=0 at outlet, others extrapolated

Can anyone tell me the fault? thanks