Aerodynamic Shape Optimization Techniques Based On Control Theory

This paper reviews the formulation and application of optimization techniques based on control theory for aerodynamic shape design in both inviscid and viscous compressible ow. The theory is applied to a system de ned by the partial di erential equations of the ow, with the boundary shape acting as the control. The Frechet derivative of the cost function is determined via the solution of an adjoint partial di erential equation, and the boundary shape is then modi ed in a direction of descent. This process is repeated until an optimum solution is approached. Each design cycle requires the numerical solution of both the ow and the adjoint equations, leading to a computational cost roughly equal to the cost of two ow solutions. Representative results are presented for viscous optimization of transonic wing-body combinations and inviscid optimization of complex con gurations.