Abstract
Natural convection in differentially heated enclosures is a benchmark problem used to investigate the physics of buoyant flows and to validate numerical methods. Such configurations are also of interest in engineering applications such as cooling of electronic components and air flow around buildings. In this work a spectral element method is used to carry out direct numerical simulations of natural convection in a tall enclosure of aspect ratio 4 with isothermal vertical walls and adiabatic horizontal walls. Spectral element methods combine the flexibility of classical finite element methods with the high accuracy and efficiency of single-domain spectral methods. The flow is solved in a three-dimensional domain with periodic boundary conditions imposed in the third direction. The numerical results are compared with solutions available in the literature and with numerical results obtained using a commercial software that employs a low-order finite volume method. Good agreement with previous work is obtained for the value of the Rayleigh number investigated, Ra = 2E9, which is greater than the critical value of Ra where transition to an unsteady, chaotic state is known to occur. The results are presented in terms of the time-averaged flow structure, Reynolds stresses and modal energies. Although the time-averaged velocity and temperature fields obtained with a commercial finite volume code are in general good agreement with the results obtained with the spectral element code, it does not give accurate predictions of second-order statistics.