Maintaining symmetry on a staggered cartesian grid,
 

Hi all, I'm using a 2D staggered cartesian grid to model a simple flow over a cylinder.

This is equivelent to a finite volume method, each volume element, consits of a pressure at the center p, a horizontal velocity at the western wall u, and a vertical velocity at the southern wall v,

I have enforced the following velocity boundary confitions,

If southern wall solid is solid
v=vobj

if western wall is solid
u=uobj

else calculate as velocity as normal.

And I am enforcing the pressure boundary conditions,

where n is the direction normal to the boundary, and F is the function such that,


However the results I am getting seem to favour a positive lift coeficient, no doubt due to the lack of symmetry, and tends to settle on a steady state flow when it shouldent

The model otherwise agrees well with benchmark solutins

Is there an easy way to regain symetry? or do I need more sophisticated boundary handeling?