Numerical modeling of the two-dimensional Rayleigh-Benard convection

We study Rayleigh-Bénard convection which is a type of natural convection occurring in a plane horizontal layer of viscous fluid heated from below and cooled from above, in which the fluid develops a regular pattern of convection cells known as Benard cells. The process of rotation is described by a system of nonlinear differential Oberbeck-Boussinesq equations. As convection parameters, the Rayleigh number and the Prandtl number are taken. The system is solved using the finite element method by FEniCS. We obtain numerical results for varying Rayleigh numbers and study the dependence of the Nusselt number on the Rayleigh number.