Systematic continuous adjoint approach to viscous aerodynamic design on unstructured grids

A continuous adjoint approach to aerodynamic design for viscous compressible flow on unstructured grids is developed. Sensitivity gradients are computed using tools of shape deformation of boundary integrals. The resulting expressions involve second-order derivatives of the flow variables that require numerical solvers with greater than second-order accuracy. A systematic way of reducing the order of these terms is presented. The accuracy of the sensitivity derivatives is assessed by comparison with finite-difference computations, and the validity of the overall methodology is illustrated with several design examples.