A Newton-Krylov algorithm is presented for aerodynamic shape optimization in three dimensions using the Euler equations. An inexact-Newton method is used in the flow solver, a discrete-adjoint method to compute the gradient, and the quasi-Newton optimizer to find the optimum. A Krylov subspace method with approximate-Schur preconditioning is used to solve both the flow equation and the adjoint equation. Basis spline surfaces are used to parameterize the geometry, and a fast algebraic algorithm is used for grid movement. Accurate discrete-adjoint gradients can be obtained in approximately one-fourth the time required for a converged flow solution. Single- and multi-point lift-constrained drag minimization optimization cases are presented for wing design at transonic speeds. In all cases, the optimizer is able to efficiently decrease the objective function and gradient for problems with hundreds of design variables.
| Identifer | oai:union.ndltd.org:TORONTO/oai:tspace.library.utoronto.ca:1807/24811 |
| Date | 30 August 2010 |
| Creators | Leung, Timothy |
| Contributors | Zingg, David W. |
| Source Sets | University of Toronto |
| Language | en_ca |
| Detected Language | English |
| Type | Thesis |
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