Multipoint and multi-objective aerodynamic shape optimization

A gradient-based Newton-Krylov algorithm is presented for the aerodynamic shape optimization of single- and multi-element airfoil configurations. The flow is governed by the compressible Navier-Stokes equations in conjunction with a one-equation transport turbulence model. The preconditioned generalized minimal residual method is applied to solve the discrete-adjoint equation, which leads to a fast computation of accurate objective function gradients. Optimization constraints are enforced through a penalty formulation, and the resulting unconstrained problem is solved via a quasi-Newton method. The new algorithm is evaluated for several design examples, including the lift enhancement of a takeoff configuration and a lift-constrained drag minimization at multiple transonic operating points. Furthermore, the new algorithm is used to compute a Pareto front based on competing objectives, and the results are validated using a genetic algorithm. Overall, the new algorithm provides an efficient approach for addressing the issues of complex aerodynamic design.