Dear sir: I took pseudo-compressibility idea to process the continuity equation, Can I also used the non-staggered grid Method(By: Rhie C M ,Chow W L, 1983) now?

The pseudo-compressibility method is mostly implemented on non-staggered grid because the P and V are coupled ,the method is free of compatability constraint which is encountered in other Poisson type methods, and is flexiable in complex geometries.

Sir: Thank you for your kind answers.

Do you mean that we can use collocated arrangement for Vi and P taking no account for the oscillating pressure field which occur in SIMPLE Method?

and, can I use the central diffence scheme for discretisation of the Pressue gradient item in this case?

Since you use artificial compresssiblity method, it is of hyperbolic type, and upwind scheme is preferable for all inviscid terms. A central scheme will lead to instability on collocated grid.

You need to be sure that you mean "collocated" and not "colocated."

Colocated means that the velocities and pressure are evaluated at the same point (as opposed to a "staggered" location scheme).

Collocated is a mathematical term - I think (and will be corrected!) that it has to do with interpolation or as method to solve ODE's.

From the context of your posts, you are probably talking about "colocated."