Efficiency and accuracy aspects of a full-multigrid SIMPLE algorithm for three-dimensional flows

This article reports on the analysis of efficiency and accuracy of a full-multigrid SIMPLE algorithm for three-dimensional flows using co-located grids and central difference discretization for both convective and diffusive fluxes. It is shown that the central differencing scheme-contrary to common belief-offers both good convergence properties and high accuracy, even at large Peclet numbers. Accurate solutions, with discretization errors below 0.5%, were obtained for lid-driven flows in a cubic cavity using grids with up to 128(3) (nearly 2.1 million) control volumes. For a grid with 64(3) (262,114) control volumes, solution can be obtained on a personal computer in 5-10 min. The computer code used for the calculations reported here is available from authors on request (free of charge).