Multigrid solution of the incompressible Navier-Stokes equations for three-dimensional recirculating flow: coupled and decoupled smoothers compared

Abstract

A comparison of multigrid methods for solving the incompressible Navier-Stokes equations in three dimensions is presented. The continuous equations are discretised on staggered grids using a second-order monotonic scheme for the convective terms and implemented in defect correction form. The convergence characteristics of a decoupled method (SIMPLE) are compared with those of the cellwise coupled method (SCGS). The convergence rates obtained for computations of the three-dimensional lid-driven cavity problem are found to be very similar to those obtained for computations of the corresponding two-dimensional problem with comparable grid density. Although the convergence rate of SCGS is thus superior to that of SIMPLE, the decoupled method is found to be more efficient computationally and requires less computing time for a given level of convergence. The linewise implementation of the coupled method (CLGS) is also investigated and shown to be more efficient than SCGS, although the convergence rate and computing time required per cycle are both found to depend on the direction of sweep