Using design-parameter sensitivities in adjoint-based design environments

Over the past several years, considerable progress has been made in aerodynamic design through the use of adjoint-based solution technologies. These design systems allow one to change the surfaces of a configuration so that some objective function, such as lift-to- drag ratio or sonic boom strength, is optimized. Unfortunately, these systems change the configuration surfaces on a point-by-point basis, instead of by changing the design parameters that were used to generate the original configuration; this limitation arose from the lack of good sensitivity calculations through the geometric design process. The objective of this paper is to demonstrate the coupling of recently developed configuration sensitivity calculations with the adjoint-based optimization frameworks. In particular, a wing is optimized to minimize the induced drag (for a fixed lift) through both the CART3D and FUN3D design frameworks. Several methods for propagating sensitivity information into the interior of Faces were investigated. The optimized results, both for sensitivities computed by finite differences (which are nearly identical to the predicted displacement field but expensive to compute) and for sensitivities computed analytically (which disagree with the predicted displacements but are inexpensive to compute), are nearly identical.