Optimal numerical strategy for unsteady natural convection in two and three dimensions

Abstract

Analyses of accuracy and computational cost of finite difference methods in computational fluid dynamics have illustrated a criterion for the minimum order for efficient calculations. This criterion favours the use of higher than second order methods when modelling greater than two space-time dimensions. These analyses have assumed the dominant length scale to be homogeneous throughout the model domain. Natural convection in a cavity can exhibit inhomogeneity of the smallest dominant length scales in identifiable sub-domains. Any inhomogeneity of this nature is shown to have a significant impact on the computational efficiency. This extended analysis suggests that an optimally efficient numerical calculation for unsteady natural convection requires: a non-uniform grid that complements the distribution of length scales to obtain a homogeneous non-dimensional grid scale; and a numerical order equal to or greater than the space-time dimension.