Preconditioned conjugate gradient methods for the incompressible Navier-Stokes equations

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 of using a conjugate-gradient-type method with an incomplete LU factorization preconditioner for two-dimensional incompressible viscous flow 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.