From Analysis to Design of High-lift Configurations Using a Newton–krylov Algorithm

An efficient multi-block Newton–Krylov algorithm using the compressible Navier–Stokes equations is presented for the analysis and design of high-lift airfoil configurations. The preconditioned generalized minimum residual (GMRES) method is applied to solve the discreteadjoint equation, leading to a fast computation of accurate objective function gradients. Furthermore, the GMRES method is used in conjunction with an inexact-Newton approach to obtain fast solutions of the Navier–Stokes equations. Optimization constraints are enforced through a penalty formulation, and the resulting unconstrained problem is solved via a quasi-Newton method. Several design examples are provided which demonstrate that this algorithm provides an effective and practical tool for the design of multi-element airfoil configurations.