A NONLINEAR MULTIGRID METHOD FOR THE 3-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

A nonlinear multigrid method is developed for solving the three-dimens ional Navier-Stokes equations in conjunction with the artificial compr essibility formulation. The method is based on the full multigrid (FMG )-full approximation storage (FAS)-algorithm and is realized via an '' unsteady-type'' procedure, according to which the equations are not so lved exactly on the coarsest grid, but some pseudo-time iterations are performed on the finer grids and some on the coarsest grid. The multi grid method is implemented in conjunction with a third-order upwind ch aracteristics-based scheme for the discretization of the convection te rms, and the fourth-order Runge-Kutta scheme for time integration. The performance of the method is investigated for three-dimensional flows in straight and curved channels as well as flow in a cubic cavity. Th e multigrid acceleration is assessed in contrast to the single-grid an d mesh-sequencing algorithms. The effects of various multigrid compone nts on the convergence acceleration, such as prolongation operators, a s well as pre- and postrelaxation iterations, are also investigated. ( C) 1998 Academic Press.