23rd Congress of International Council of the Aeronautical Sciences, 8-13 September, 2002, Toronto, Canada
Paper ICAS 2002-1.7.3

FROM ANALYSIS TO DESIGN OF HIGH-LIFT CONFIGURATIONS USING A NEWTON-KRYLOV ALGORITHM

M. Nemec, D. W. Zingg
University of Toronto, Canada

Keywords: optimal shape design, airfoil, navier–stokes, high-lift, discrete gradient, adjoint, flow sensitivities, newton’s method, gmres

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 discrete-adjoint 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.

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