Boundary Optimal Control of Natural Convection by Means of Mode Reduction

Abstract

We consider problems of controlling the intensity of the Rayleigh-Bénard convection by adjusting the heat flux distribution at the boundary while keeping the heat input the same. The Karhunen-Loève Galerkin procedure is used to reduce the Boussinesq equation to a low dimensional dynamic model, which in turn is employed in a projected gradient method to yield the optimal heat flux distribution. The performance of the Karhunen-Loève Galerkin procedure is assessed in comparison with the traditional technique employing the Boussinesq equation, and is found to be very accurate as well as efficient.