Aerodynamic Shape and Planform Optimization of Wings Using a Viscous Reduced Adjoint Gradient Formula

in the calculation of the complete gradient is e#ectively independent of the number of design variables. In the control theory approach the necessary gradients are obtained via the solution of the adjoint equations of the governing equations of interest. The only cost involved is the calculation of one flow solution and one adjoint solution whose complexity is similar to that of the flow solution. The present work builds on the foundation of control theory for systems governed by partial di#erential equations originally laid out by J.L. Lions and first used in transonic flow by Jameson. In fact, the method has even been successfully used for the aerodynamic design of complete aircraft configurations. Recently the authors have also included wing planform as design variables and have successfully designed a wing of the aircraft configuration which produces a specified lift with minimum drag, while meeting other criteria such as low structure weight, su#cient fuel volume, and s