Natural convection in a shallow laterally heated air‐filled cavity

Abstract

AbstractThe flow in a shallow, laterally heated air‐filled cavity is investigated numerically using a primitive variable formulation of the governing equations of motion. Solutions are obtained for the entire flow field using a coupled solver combined with an FAS non‐linear multigrid convergence accelerator. While care is taken to use a high‐order, bounded discretization scheme for convective transport, the overall stability and efficiency of the approach is enhanced through the use of defect correction. This combination of features enables solutions to be found on extremely fine grids. Results for the flow in the end region of such cavities are compared qualitatively with the predictions of asymptotic 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 103 to 108. Finally it is demonstrated how such solutions can be further enhanced by using locally refined grids in the end regions.