Abstract
An additive-correction multigrid method for the prediction of two-dimensional unsteady flows, described in a previous article, is applied to selected cavity flow problems. The cases considered are the lid-driven cavity problem and the buoyant flow in differentially heated cavities. Accurate results are obtained for the lid-driven cavity, where fine-grid, high-Reynolds-number calculations, indicate that the steady flow bifurcates to a periodic regime for a Reynolds value in the range 7,500--10,000. The results for side-heated rectangular enclosures are presented first for a Prandtl number equal to zero, and corresponding values of Grashof number of 1.2 {times} 10{sup 5} and 1.6 {times} 10{sup 5}. In addition, a Prandtl number of 0.71 is considered, with values of the Rayleigh number of 1 {times} 10{sup 8}, 2 {times} 10{sup 8}, and 2 {times} 10{sup 9}. The study demonstrates that the additive-correction multigrid method is computationally efficient, and is capable of performing accurate simulations of time-dependent, and possibly chaotic, flows in enclosures.
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