Aerodynamic Shape Optimization of Wings Using a Parallel Newton-Krylov Approach

Abstract

A Newton-Krylov algorithm for aerodynamic shape optimization in three dimensions is presented for both single-point and multipoint optimization. An inexact Newton method is used to solve the Euler equations, a discrete adjoint method is used to compute the gradient, and an optimizer based on a quasi-Newton method is used to find the optimal geometry. The flexible generalized minimal residual method is used with approximate Schur preconditioning to solve both the flow equation and the adjoint equation. The wing geometry is parameterized by B-spline surfaces, and a fast algebraic algorithm is used for grid movement at each iteration. An effective strategy is presented to enable simultaneous optimization of planform variables and section shapes. Optimization results are presented with up to 225 design variables to demonstrate the capabilities and efficiency of the approach.