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

摘要

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 termsand 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-drivencavity 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 isfound 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 convergencerate and computing time required per cycle are both found to depend on the direction of sweep. The optimal implementation of CLGS is found to be only marginally more effective than SIMPLE, but a change to the structure of the data storage would increasethe advantage.