3D Numerical Simulation of Rayleigh-Bénard Convection in a Cylindrical Container

The heat transport by natural convection is a central mechanism in the explanation of many natural phenomena. Despite many existing work on the Rayleigh-Bénard convection, often the phenomenon is studied by making a two-dimensional approach or using a rectangular container. In this work, we solve numerically the Navier-Stokes, continuity and energy equations in cylindrical coordinates. To this end a finite difference scheme is used for the time and spatial coordinates \(r\) and \(z\), whereas a Fourier spectral method is used for the angular coordinate. The advantage of this procedure is that it can be easily parallelized. The numerical results include the formation of concentric rolls and other patterns, which are compared with experimental results reported in the literature.