BOUNDARY CONTROL FOR NON-ISOTHERMAL NAVIER-STOKES FLOWS BY USING DOMAIN DECOMPOSITION AND EXTENDED FLOW METHODS

Abstract. In this work we study a class of stationary optimal temperature and optimal flow control problems described by velocity, pressure and temperature where the optimal design of these systems is reached by controlling the boundary conditions. The optimal boundary control problem is transformed into an extended distributed problem and then solved by using standard distributed control techniques over the extended part of the do-main. The coupled multigrid solver for the optimality system is based on a local Vanka-type solver for the non-isothermal Navier-Stokes and adjoint system. The solution is achieved by solving and relaxing element by element the optimal control problem which is formulated by using an embedded domain approach. By using this technique only local subsystems are stored and solved which allows this method to be very effective in large problems where other solvers cannot satisfy memory and cpu requirements. Also the adjoint and the orig-inal system can be solved exactly over small domains leading to a very robust optimization. Some numerical examples of boundary controls are presented.