Date of Award

Summer 2004

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical Engineering

Committee Director

Arthur C. Taylor, III

Committee Member

Gene Hou

Committee Member

Perry A. Newman

Committee Member

Surendra N. Tiwari


This study investigates and demonstrates a methodology for uncertainty propagation and robust design in Computational Fluid Dynamics (CFD). Efficient calculation of both first- and second-order sensitivity derivatives is requisite in the proposed methodology. In this study, first- and second-order sensitivity derivatives of code output with respect to code input are obtained through an efficient incremental iterative approach.

An approximate statistical moment method for uncertainty propagation is first demonstrated on a quasi one-dimensional (1-D) Euler CFD code. This method is then extended to a two-dimensional (2-D) subsonic inviscid model airfoil problem. In each application, given statistically independent, random, normally distributed input variables, a first- and second-order statistical moment matching procedure is performed to approximate the uncertainty in the CFD output. In each model problem, a Sensitivity Derivative Enhanced Monte Carlo (SDEMC) method is also demonstrated. With this methodology, incorporation of the first-order sensitivity derivatives into the data reduction phase of a conventional Monte Carlo (MC) simulation allows for improved accuracy in determining the first moment of the CFD output. The statistical moment method and the SDEMC method are also incorporated into an investigation of output function variance. The methods that exploit the availability of sensitivity derivatives are found to be valid and computationally efficient when considering small deviations from input mean values.

In both the 1-D and 2-D problems, uncertainties in the CFD input variables are incorporated into robust optimization procedures. For each optimization, statistical moments involving first-order sensitivity derivatives appear in the objective function and system constraints. The constraints are cast in probabilistic terms; that is, the probability that a constraint is satisfied is greater than or equal to some desired target probability. Gradient-based robust optimization of this stochastic problem is accomplished through use of both first and second-order sensitivity derivatives. For each robust optimization, the effect of increasing both input standard deviations and target probability of constraint satisfaction are demonstrated. This method provides a means for incorporating uncertainty when considering small deviations from input mean values.