Application of SIMPLE method for solving steady state NS equation
 

Hi every one,
I am trying to model the developing incompressible steady state flow between flat plates (Poiseuille flow) in MATLAB. Staggered grid approach is used. The chosen boundary conditions are as follows:
Extents of the domain: 0<x< L 0< y< h
top and bottom @ y=0& y=h
u=v=0 dp/dy=0
at left boundary @ x=0
v=0, u=const. (uniform across the boundary)
p1=p2-(p3-p2)*0.5 x=0;
at the right boundary@x=L
dp/dx=0, du/dx=0, dv/dx=0
SIMPLE procedure was used for solving the equation and iterations.
The problem is that the pressure correction equation is not giving a unique solution. I have checked the equations and it satisfies the boundary condition and discretisation procedure. I want to know how to correct the pressure correction equation. Pressure correction at the right boundary is zero. I have a taken a linear pressure profile as my initial guess for the problem. So, the pressure correction for the grid points in the top and bottom boundary is same as the pressure correction of the adjacent nodes in the Y direction. Kindly suggest possible corrections and prospective deviations in the method. :)