Solution of Transient Laminar Natural Convection in a Square Cavity by an Explicit Finite Element Scheme

This paper discusses the application of a finite element method based on the first-order projection scheme, which is an extension ofChorin's algorithm, to transient laminar natural convection in a square cavity. Results have been presented for a fluid of Prandtl number 0.71 in the Rayleigh number range of 103-106 in terms of the variation of vertical velocity component, nondimensional temperature, and average Nusselt number with time. Various features of the scheme that render it economical in terms of CPU time and storage requirements are discussed. The steady state results have been compared with benchmark solutions, and the agreement appears to be good.