Optimal Control of Thermally Convected Fluid Flows

We examine the optimal control of stationary thermally convected uid ows from the theoretical and numerical point of view. We use thermal convection as control mechanism, that is, control is eeected through the temperature on part of the boundary. Control problems are formulated as constrained minimization problem. Existence of optimal control is given and a rst order necessary conditions of opti-mality from which optimal solutions can be obtained is established. We develop numerical methods to solve the necessary conditions of optimality and present computational results for control of cavity and channel type ows showing the feasibility of the proposed approach.