Finite element simulation of three-dimensional Rayleigh-Benard convection

The application of a finite element scheme to three-dimensional Rayleigh-Benard convection in a horizontal fluid layer heated from below is presented. The scheme is based on the Petrov-Galerkin weak formulation using exponential weighting functions. The incompressible Navier-Stokes equations and energy equation with the Boussinesq approximation are numerically integrated in time by using a fractional step strategy with second-order accurate Adams-Bashforth scheme for both convection and diffusion terms. Numerical results obtained are compared through the Rayleigh-Benard convection of air for Rayleigh numbers up to 87300 with the experimental data and other existing numerical data, and demonstrate the workability and validity of the present approach.