Preconditioned conjugate gradient methods for the incompressible NavierStokes equations
Abstract
A robust technique for solving primitive variable formulations of the incompressible NavierStokes 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 conjugategradienttype method with an incomplete LU factorization preconditioner for twodimensional 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.
 Publication:

International Journal for Numerical Methods in Fluids
 Pub Date:
 August 1992
 DOI:
 10.1002/fld.1650150303
 Bibcode:
 1992IJNMF..15..273C
 Keywords:

 Conjugate Gradient Method;
 Incompressible Flow;
 NavierStokes Equation;
 Nonlinear Equations;
 Preconditioning;
 Robustness (Mathematics);
 Fluid Mechanics and Heat Transfer