Sensitivity Evaluation in Aerodynamic Optimal Design

The possibility to compute first- and second-derivatives of functionals subject to equality constraints given by state equations (and in particular non-linear systems of Partial Derivative Equations) allows us to use efficient techniques to solve several industrial-strength problems. Among possible applications that require knowledge of the derivatives, let us mention: aerodynamic shape optimization with gradient-based descent algorithms, propagation of uncertainties using perturbation techniques, robust optimization, and improvement of the accuracy of a functionnal using the adjoint state. In this work, we develop and analyze several strategies to evaluate the first- and second-derivatives of constrained functionals, using techniques based on Automatic Differentiation. Furthermore, we propose a descent algorithm for aerodynamic shape optimization, that is based on techniques of multi-level gradient, and which can be applied to different kinds of parameterization.