Abstract: The splitting difference scheme is used to study flow separation. Flows behind a Circular Cylinder are computed as a model problem. In view of the nature of the flows, the variables are transformed. The boundary condition for pressure is given by intermediate velocity. The velocity boundary Conditions on the rigid wall of free-slip are given by interpolation. The multigrid algorithm is applied to the Pressure iteration. We also Choose better initial Values for the model problem by means of the multigrid algorithm idea.