Stabilization of Rayleigh–Bénard convection by means of mode reduction

A method is developed to suppress the intensity of the Rayleigh–Bénard convection by adjusting the heat flux distribution at the bottom boundary under the constraint of constant heat input to the system. The appropriate profile of heat flux, which is changing continually in accordance with the shape of convection cells in the domain, is determined by the model predictive control. The optimal control strategy given by the model predictive control is implemented efficiently by employing the Karhunen–Loéve Galerkin procedure through which the Boussinesq equation is reduced to a low–dimensional dynamic model. This method is found to yield accurate results with a decent requirement of computer time.