A set of complete two- and three-dimensional direct numerical simulations (DNS) in a differentially heated air-filled cavity of aspect ratio 4 with adiabatic horizontal walls is presented in this paper. Although the physical phenomenon is three-dimensional, owing to its prohibitive computational costs the majority of the previous DNS of turbulent and transition natural convection flows in enclosed cavities assumed a two-dimensional behaviour. The configurations selected here (Rayleigh number based on the cavity height 6.4 × 108, 2 × 109 and 1010, Pr = 0.71) are an extension to three dimensions of previous two-dimensional problems.An overview of the numerical algorithm and the methodology used to verify the code and the simulations is presented. The main features of the flow, including the time-averaged flow structure, the power spectra and probability density distributions of a set of selected monitoring points, the turbulent statistics, the global kinetic energy balances and the internal waves motion phenomenon are described and discussed.As expected, significant differences are observed between two- and three-dimensional results. For two-dimensional simulations the oscillations at the downstream part of the vertical boundary layer are clearly stronger, ejecting large eddies to the cavity core. In the three-dimensional simulations these large eddies do not persist and their energy is rapidly passed down to smaller scales of motion. It yields on a reduction of the large-scale mixing effect at the hot upper and cold lower regions and consequently the cavity core still remains almost motionless even for the highest Rayleigh number. The boundary layers remain laminar in their upstream parts up to the point where these eddies are ejected. The point where this phenomenon occurs clearly moves upstream for the three-dimensional simulations. It is also shown that, even for the three-dimensional simulations, these eddies are large enough to permanently excite an internal wave motion in the stratified core region. All these differences become more marked for the highest Rayleigh number.

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The numerical simulation of time-accurated complex ows needs large computational resources. For the case of incompressible ows, the solution of the pressure-correction equation is typically the main bottleneck, especially on loosely coupled parallel computers such as PC clusters. An algorithm intended to solve this problem is presented. It is a variant of the Schur complement method that uses direct solvers for each subdomain and for the interface equation. The inverse of the interface matrix is evaluated and stored in parallel. Simulation of turbulent natural convection is used as a benchmark to show its potential and limitations.