An iterative stabilized fractional step algorithm for numerical solution of incompressible N-S equations

Abstract

SUMMARY Stabilized fractional step algorithm has been widely employed for numerical solution of incompressible Navier-Stokes equations. However, smaller time step sizes are required to use for existing explicit and semi-implicit versions of the algorithm due to their fully or partially explicit nature particularly for highly viscousow problems. The purpose of this paper is to present two modied versions of the fractional step algorithm using characteristic based split and Taylor-Galerkin like based split. The proposed modied versions of the algorithm are based on introducing an iterative procedure into the algorithm and allow much larger time step sizes than those required to the preceding ones. A numerical study of stability at acceptable convergence rate and accuracy as well as capability in circumventing the restriction imposed by the LBB condition for the proposed iterative versions of the algorithm is carried out with the plane Poisseuilleow problem under dierent Reynolds numbers ranging from low to high viscosities. Numerical experiments in the plane Poisseuilleow and the lid- driven cavityow problems demonstrate the improved performance of the proposed versions of the algorithm, which are further applied to numerical simulation of the polymer injection moulding process. Copyright ? 2005 John Wiley & Sons, Ltd.