SOLUTION OF THE PRESSURE CORRECTION EQUATION BY THE PRECONDITIONED CONJUGATE-GRADIENT METHOD

The purpose of this work is to study the use of a preconditioned conju gate gradient method for solving the pressure correction equation in t he simulation of incompressible flows. The preconditioners considered in this work include SSOR, ILU, and MILU. In addition, a new precondit ioner Based on an ADI-type iterative scheme is presented. The ADI sche me uses the concept of the splitting of matrix via local one-dimension ality and is economical in memory requirement. A guideline for choosin g the optimum parameter of ADI preconditioner is offered and tested. T hese preconditioners are tested in the simulation of lid-driven cavity flow and backward-facing step flows. The test results show that both ILU- and SSOR-preconditioned conjugate gradient methods have very irre gular early-stage convergence. Both MILU- and ADI-preconditioned CG me thods can be made very stable by choosing adequate parameters. The goo d convergence stability comes with lower asymptotic convergence rate.