Preconditioned conjugate gradient methods for incompressible Navier-Stokes equations

Abstract

A robust technique for solving primitive-variable formulations of the incompressible Navier-Stokes equations is to use Newton iteration for the fully-implicit nonlinear equations. A direct sparse matrix method can be used to solve the Jacobian but is costly for large problems; an alternative is to use an iterative matrix-method. This paper investigates effective ways to use a conjugate gradient type method with an incomplete LU factorization preconditioner for two-dimensional incompressible viscous oow problems. Special attention is paid to the ordering of unknowns, with emphasis on a minimum updating matrix (MUM) ordering. Numerical results are given for several test problems.