An improved time-splitting method for simulating natural convection heat transfer in a square cavity by Legendre spectral element approximation

Abstract

A Legendre spectral element formulation of an improved time-splitting method is developed for the natural convection heat transfer problem in a square cavity. The convection term, Stokes term and temperature diffusion term are considered separately. The standard Galerkin variation is applied for the convection and temperature diffusion term, and the least-squares variation is adopted to the Stokes term due to the inf-sup constraint. Therefore, assumptions about the intermediate velocity and pressure in the original time-splitting method is eliminated, and the final velocity is divergence free. The numerical test verifies the validation and the h−p convergence characteristics of this method. Besides, the natural convection heat transfer in a square cavity with the Rayleigh number ranging in 103–106 is simulated, and the numerical solutions reach an satisfactory agreement with existing both numerical and experimental results. Furthermore, the natural convection in a square cavity with four heat sources is investigated, depicting a further application of this method.