This paper describes the application of the Modified Interpolating Matrix Method (IMM) to the calculation of incompressible viscous flows using a stream function-vorticity formulation of the two-dimensional steady Navier-Stokes equations. The IMM is coupled with second-order approximations for vorticity boundaries. The fundamental concepts of the formulation and the associated solution strategy used are described in technical detail. There are two tests case chosen for the performance evaluation of this strategy. The first involves the lid-driven square cavity flow at Reynolds numbers varying from 1000 to 10000, the second involves the lid-driven in inclined cavity with inclination angle 45°, 30° and 15° at Reynolds numbers of 100 and 1000, respectively. Our numerical solutions are compared with the solutions found in the literature, and good agreement is found.

finite difference, IMM, Lax-Wendroff scheme, non-orthogonal grid, benchmark problems.