An elliptic grid generation technique for the flow contraction

In this paper, we determined a numerical solution of the incompressible Navier-Stokes equations for the flow inside the contraction geometry. The governing equations are written in the vorticity-stream function formulations. The numerical solution is based on a technique of automatic numerical generation of a curvilinear coordinate system by transforming the governing equation into computational plane. The transformed equations are approximated using central differences and solved simultaneously by successive over-relaxation iteration.