@PhDThesis{ itlic:2003-012,
author = {Olivier Amoignon},
title = {Adjoint-Based Aerodynamic Shape Optimization},
school = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2003},
number = {2003-012},
type = {Licentiate thesis},
month = oct,
note = {In the first printed version, many references to the
bibliography are off by one. The online version does not
have this error},
abstract = {An adjoint system of the Euler equations of gas dynamics
is derived in order to solve aerodynamic shape optimization
problems with gradient-based methods. The derivation is
based on the fully discrete flow model and involves
differentiation and transposition of the system of
equations obtained by an unstructured and node-centered
finite-volume discretization. Solving the adjoint equations
allows an efficient calculation of gradients, also when the
subject of optimization is described by hundreds or
thousands of design parameters.
Such a fine geometry description may cause wavy or
otherwise irregular designs during the optimization
process. Using the one-to-one mapping defined by a Poisson
problem is a known technique that produces smooth design
updates while keeping a fine resolution of the geometry.
This technique is extended here to combine the smoothing
effect with constraints on the geometry, by defining the
design updates as solutions of a quadratic programming
problem associated with the Poisson problem.
These methods are applied to airfoil shape optimization for
reduction of the wave drag, that is, the drag caused by gas
dynamic effects that occur close to the speed of sound. A
second application concerns airfoil design optimization to
delay the laminar-to-turbulent transition point in the
boundary layer in order to reduce the drag. The latter
application has been performed by the author with
collaborators, also using gradient-based optimization.
Here, the growth of convectively unstable disturbances are
modeled by successively solving the Euler equations, the
boundary layer equations, and the parabolized stability
equations.}
}