Finite volume discretization method are applied to solve the incompressible Navier-Stokes equations with primitive variables in a non-dimensional form, multigrid techniques were used to simulate the two-dimensional square driven cavity with small to large Reynolds numbers. The flow problem of constant velocity from right to left of a square cavity is considered and obtained a numerical solutions on 3 grid levels, having 32x32, 64x64 and 128X128 cells. Reynolds number of 1x102 , 1x103 was selected for laminar flow and 8x103 , 12x103 was selected for turbulent flow. At low and high Reynolds numbers, numerical solutions for square driven cavity flow are obtained and their results are compared to those obtained by other researchers using different approximation methods.

Keywords : Incompressible Navier-Stokes Equations, Finite Volume Method, Square Driven Cavity Problem, Discretization, Internal Flow