Optimal control of thermal fluid flow using automatic differentiation

Abstract

The aim of this study is to present a method for numerical optimal control of thermal fluid flow using automatic differentiation (AD). For the optimal control, governing equations are required. The optimal controls that have been previously presented by the present authors’ research group are based on the Boussinesq equations. However, because the numerical results of these equations are not satisfactory, the compressible Navier–Stokes equations are employed in this study. The objective is to determine whether or not the temperature at the objective points can be kept constant by imposing boundary conditions and by controlling the temperature at the control points. To measure the difference between the computed and target temperatures, the square sum of these values is used. The objective points are located at the center of the computational domain while the control points are at the bottom of the computational domain. The weighted gradient method that employs AD for efficiently calculating the gradient is used for the minimization. By using numerical computations, we show the validity of the present method.