Non-parametric aerodynamic shape optimization

Abstract

Numerical schemes for large scale shape optimization are considered. Exploiting the structure of shape optimization problems is shown to lead to very efficient optimization methods based on non-parametric surface gradients in Hadamard form. The resulting loss of regularity is treated using higher order shape Newton methods where the shape Hessians are studied using operator symbols. The application ranges from shape optimization of obstacles in an incompressible Navier–Stokes fluid to super- and transonic airfoil and wing optimizations.