NUMERICAL ERRORS OF THE GALERKIN FINITE-ELEMENT METHOD FOR NATURAL CONVECTION OF A FLUID LAYER OR A FLUID-SATURATED POROUS LAYER

Abstract

This paper describes the effects of element size and formula used for the calculation of temperature gradients on the local and average Nusselt numbers of natural convection for the widely used Galerlan finite-element method. Two cases of laminar two-dimensional natural convection are examined, namely, a fluid layer and a porous layer. The numerical error in the Nusselt numbers decreases with decreasing element size. The maximum error occurs at the position of a maximum of the local Nusselt number. In addition to the effect of element size, the Nusselt numbers are shown to vary with the formula used for calculating temperature gradients. The Nusselt numbers extrapolated to zero element size for different formulas are found, in both cases, to be virtually identical and also to agree well with the experimental data and the results computed by finite-difference methods