Date of Award

Spring 2007

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematics and Statistics


Computational and Applied Mathematics

Committee Director

Fang Q. Hu

Committee Member

Mehdi R. Khorrami

Committee Member

Hideaki Kaneko

Committee Member

Richard Noren

Committee Member

Ruhai Zhou


Aircraft airframe noise pollution resulting from the take-off and landing of airplanes is a growing concern. Because of advances in numerical analysis and computer technology, most of the current noise prediction methods are computationally efficient. However, the ability to effectively apply an approach to complex airframe geometries continues to challenge researchers. The objective of this research is to develop and analyze a robust noise prediction method for dealing with geometrical modifications. This new approach for determining sound pressure involves computing exact, or tailored, Green's functions for use in acoustic analogy. The effects of sound propagation and scattering by solid surfaces are included in the exact Green's function, which is tailored for a specific geometry. The exact Green's function is computed using a spectral collocation boundary element method that can easily accommodate complex geometries. A frequency-domain spectral collocation method is applied to both smooth and non-smooth boundaries, resulting in exponential convergence on smooth boundaries. Solution singularities at boundary corners are dealt with via an exponential grading element refinement. With proper refinement, exponential convergence is also obtained for non-smooth boundaries. The formulation and application of a three-dimensional time-domain BEM allows computation of exact Green's functions for all frequencies in a single calculation. Long-time instabilities in the time-marching numerical solutions are corrected via a Burton-Miller modified integral equation. Two examples provide validation of the acoustic analogy involving the exact Green's function.





Included in

Mathematics Commons