A Newton-Krylov-Multigrid Method for the Incompressible Navier-Stokes Equations

Michael Pernice

University of Utah
Center for High Performance Computing
155 S 1452 E Rm 405
Salt Lake City, Utah 84112-0190

Michael Tocci

Department of Mathematical Sciences
Worcester Polytechnic Institute
Worcester, MA 01609


The application of an inexact Newton method to two- and three-dimensional flows is described. Robustness and efficiency of the method is largely determined by the preconditioner. A linear multigrid preconditioner that employs classical pressure-correction methods as smoothers is described. The flexibility of the approach is demonstrated through application to both steady and unsteady problems; use of a low-order discretization in the preconditioner; use of mesh sequencing to address the problem of obtaining a good starting approximation for the inexact Newton method; and implementation and performance on parallel computers. -- Michael Pernice Center for High Performance Computing pernice@chpc.utah.edu http://www.chpc.utah.edu/~pernice