A study of iterative methods for Navier-Stokes equations

Maryse Page and André Garon

Département de Génie Mécanique, Ecole Polytechnique de Montréal, C.P. 6079, Succ. "A", Montréal, Canada, H3C 3A7


Abstract

A study of iterative methods is performed to compute the numerical solutions of the Navier-Stokes equations for incompressible viscous fluid flow in 3D domains. These equations are formulated in primitive variables, discretized by finite element with continuous quadratic velocity and discontinuous linear pressure approximations. To satisfy mass conservation, an augmented Lagrangian implementation of Uzawa's algorithm is used. In this algorithm, the pressure is not part of the unknowns of the discrete problem, but is updated iteratively as the nonlinear system of equations is solved. The resulting matrix is nonsymmetric, large and sparse, with high condition number. We will compare the performance of different iterative methods, like CGS, Bi-CGSTAB, QMR, GMRES(k), coupled with different preconditioning techniques (ILU(0), ILUT(p,\tau)) to solve system of equations for laminar 3D fluid flow problems.