The Solution of Pressure Correction Equation by Preconditioned Conjugate Gradient Method

Abstract

The purpose of this work is to study the use of a preconditioned conjugate gradient method for solving the pressure correction equation in the simulation of incompressible flows. The preconditioned considered in this work include SSOR, ILU, and MIL.U. In addition, a new preconditioner based on an ADI-type iterative scheme is presented. The AD1 scheme uses the concept of the splitting of matrix via local one-dimensionality and is economical in memory requirement. A guideline for choosing the optimum parameter of ADI preconditioner is offered and tested. These preconditioned are tested in the simulation of lid-driven cavity flow and backward-facing step flows. The test results show that both ILU- and SSOR-precon-ditioned conjugate gradient methods have very irregular early-stage convergence. Both MILV- and ADI-precanditioned CC methods can be made very stable by choosing adequate parameters. The good convergence stability comes with lower asymptotic convergence rate.