New Preconditioned Group Methods for the Solution of a Coupled System of Partial Differential Equations

Abstract

The suitability of the four-point Explicit Decoupled Group (EDG) iterative method in solving a twodimensional steady-state Navier-Stokes equation was demonstrated in (Ali and Abdullah, 1999) where the iterative group scheme derived from the rotated five-point formula converges more rapidly than the standard point scheme based on the centred difference formula. The Navier-Stokes equation was considered in a stream-function and vorticity formulation which resulted in a Poisson equation coupled with a convection-diffusion equation. The numerical results were also shown to be in agreement with their theoretical computational complexity analysis. In this paper, we study the applicability of a suitable splitting-type block preconditioner applied to this group scheme as a way to further improve the convergence rate of the method in solving the steady-state Navier-Stokes equation. Several numerical experiments were carried out and the results will be discussed to confirm the superiority of the proposed method over its original unpreconditioned counterpart.