Staggered incremental unknowns for solving Stokes and generalized Stokes problems

This article is devoted to the presentation of a multilevel method using fi nite differences that is well adapted for solving Stokes and Navier-Stokes problems in primitive variables. We use Uzawa type algorithms to solve the saddle point problems arising from spatial discretization by staggered grid s and a semi-explicit temporal scheme. By means of a new change of basis op erator, the two-dimensional velocity and pressure fields of an M.A.C mesh a re gathered in a hierarchical order, into several grids preserving the M.A. C property on each of them. These new hierarchical unknowns, called Stagger ed Incremental Unknowns (SIU), allow us to develop techniques which reduce the cost of the resolution of either Stokes or generalized Stokes problems. An experimental estimation of the condition number of the inner matrix is given, and justifies the preconditioning effect of the staggered incrementa l unknowns. (C) 2000 IMACS. Published by Elsevier Science B.V. All rights r eserved.