1. In the mid-1970s, the use of numerical optimization techniques for the design of aircraft components was explored.27"29These early studies focused primarily on airfoil and wing design using the lower-fidelity nonlinear transonic small-disturbance equation or the full-potential equation for the analyses, and used finite difference calculations for gradient information. These analyses were limited in their ability to accurately predict nonlinear phenomena. Also during this time, uses of optimal control techniques were being explored, in incompressible viscous flows, to obtain analytical gradients.30"32In the early 1980s, Angrand33applied these optimal control techniques to compressible potential flow equations for twodimensional airfoils. These techniques and the early French studies are discussed by Pironneau.34Independently, Jameson2advocated and used control-theory techniques in aerodynamic design via CFD.
2. Newman et al.89developed a two-dimensional, and later a three-dimensional,57second-order spatially accurate discrete sensitivity analysis approach that has been used to perform the inviscid design optimization of airfoils and transport wings in transonic flow. Included in Refs. 57 and 89 are optimization results from a limited study of the influence of spatial accuracy for both the state equations and sensitivity analyses. More recently, Newman41and Newman et al.58presented the shape sensitivity analysis and design optimization of a subsonic, high angle-of-attack, multielement airfoil and of a full Boeing 747-200 aircraft. In the work of Refs. 57, 58, and 89, the unstructured-grid sensitivities with respect to the geometric design variables are evaluated by differentiating the grid adaptation and surface parameterization routines with ADIFOR. Once the shape-sensitivity analysis code has been developed, the only modules that change from one configuration to another are these surface parameterization routines. Hence, utilizing ADIFOR for this purpose provided an efficient and accurate means of studying various geometries.
3. Discrete shape sensitivity equations for aerodynamic problems