NATURAL-CONVECTION IN A SHALLOW LATERALLY HEATED AIR-FILLED CAVITY

The how in a shallow, laterally heated air-filled cavity is investigat ed numerically using a primitive variable formulation of the governing equations of motion. Solutions are obtained for the entire how field using a coupled solver combined with an FAS non-linear multigrid conve rgence accelerator. While care is taken to use a high-order, bounded d iscretization scheme for convective transport, the overall stability a nd efficiency of the approach is enhanced through the use of defect co rrection. This combination of features enables solutions to be found o n extremely fine grids. Results for the flow in the end region of such cavities are compared qualitatively with the predictions of asymptoti c theory for large aspect ratio, A (length:height), up to values of A higher than previously reported (A = 100); the particular case of A = 20 Is considered for Rayleigh numbers in the range 10(3) to 10(8). Fin ally it is demonstrated how such solutions can be further enhanced by using locally refined grids in the end regions.