Type of Document Dissertation Author Shenoy, Ajit R. URN etd-402101939761081 Title Optimization Techniques Exploiting Problem Structure: Applications to Aerodynamic Design Degree PhD Department Aerospace and Ocean Engineering Advisory Committee

Advisor Name Title Grossman, Bernard M. Herdman, Terry L. Kapania, Rakesh K. Lutze, Frederick H. Jr. Cliff, Eugene M. Committee Chair Keywords

- Sequential Quadratic Programming
- Reduced Hessian
- Trust Region
- Sparse Optimization
- Airfoil Design
Date of Defense 1997-04-11 Availability unrestricted AbstractThe research presented in this dissertation investigates the use of all-at-once

methods applied to aerodynamic design. All-at-once schemes are usually based on

the assumption of sufficient continuity in the constraints and objectives, and

this assumption can be troublesome in the presence of shock discontinuities.

Special treatment has to be considered for such problems and we study several

approaches.

Our all-at-once methods are based on the Sequential Quadratic Programming

method, and are designed to exploit the structure inherent in a given problem.

The first method is a Reduced Hessian formulation which projects the

optimization problem to a lower dimension design space. The second method

exploits the sparse structure in a given problem which can yield significant

savings in terms of computational effort as well as storage requirements. An

underlying theme in all our applications is that careful analysis of the given

problem can often lead to an efficient implementation of these all-at-once

methods.

Chapter 2 describes a nozzle design problem involving one-dimensional transonic

flow. An initial formulation as an optimal control problem allows us to solve

the problem as as two-point boundary problem which provides useful insight into

the nature of the problem. Using the Reduced Hessian formulation for this

problem, we find that a conventional CFD method based on shock capturing

produces poor performance. The numerical difficulties caused by the presence of

the shock can be alleviated by reformulating the constraints so that the shock

can be treated explicitly. This amounts to using a shock fitting technique.

In Chapter 3, we study variants of a simplified temperature control problem.

The control problem is solved using a sparse SQP scheme. We show that for

problems where the underlying infinite-dimensional problem is well-posed, the

optimizer performs well, whereas it fails to produce good results for problems

where the underlying infinite-dimensional problem is ill-posed. A transonic

airfoil design problem is studied in Chapter 4, using the Reduced SQP

formulation. We propose a scheme for performing the optimization subtasks that

is based on an Euler Implicit time integration scheme. The motivation is to

preserve the solution-finding structure used in the analysis algorithm.

Preliminary results obtained using this method are promising. Numerical results

have been presented for all the problems described.

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