Accurate solution of Navier-Stokes equations with parallel computations

3-D Viscous incompressible flows past complex shapes are studied with accurate solution to Navier-Stokes equations in cluster of workstations on PVM environment. The Finite Element Method with an explicit time marching scheme is used for solution of the momentum equations. The element-by-element (EBE) iteration technique is employed for solution of the auxiliary potential function. The parallelization procedure is considerably simple for the numerical solution of the momentum equation but it involves large amount of message passing for the auxiliary potential equation since it is solution is iterative. The Domain decomposition technique is employed for the solution of the elliptic equation. Matching and nonoverlapping grids are used for solution of both the momentum and the auxiliary potential equations. The cavity problem is solved for 2, 4 and 6 domains having equal number of grid points. The speed ups and overall efficiencies obtained are more than satisfying.