Abstract: The paper presents a high accurate method for two dimensional incompressible viscous complex flow. Governing equations are used to adopt primitive variables and the formulation of Poisson equation for pressure. The Navier Stokes equation is solved by fourth order accurate compact scheme making as block tridiagonal linear equations for space and the ADI method for time advance in the general non staggered grid system, and the SOR method solves Poisson equation of pressure. A domain decomposition method is...