Multigrid Method Combined with Defect Correction for Free Convection Problems at High Rayleigh Numbers

摘要

The application of a multigrid method to the computation of free convection flow at high Rayleigh number is described. The differential equations are discretized by a so-called hybrid scheme, which is a combination of central and upwind differences. Convergence problems are encountered at high Rayleigh numbers. One remedy is to introduce a direct solver on the coarsest grid, and to take the coarsest grid not too coarse. Another remedy, less costly, is to introduce artificial diffusion. The resulting loss of discretization accuracy is compensated by defect correction. The discretization error, the convergence behavior and the computing time are studied by means of numerical experiments.