Date of Award

Spring 2014

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematics and Statistics


Computational and Applied Mathematics

Committee Director

Fang Q. Hu

Committee Member

Hideaki Kaneko

Committee Member

Ruhai Zhou

Committee Member

Miltiadis Kotinis


Traditionally, the acoustic source terms are modeled by single frequency sinusoidal functions. In the present study, the acoustic sources are modeled by a broadband wave packet. Radiation of acoustic waves at all frequencies can be obtained by Time Domain Wave Packet (TDWP) method in a single time domain computation. The TDWP method is also particularly useful for computations in the ducted or waveguide environments where incident wave modes can be imposed cleanly without a potentially long transient period. Theoretical analysis as well as numerical validation are performed in this study. In addition, the adjoint equations for the linearized Euler equations in the time domain are formulated for the Cartesian coordinates Analytical solution for adjoint equations is derived by using Green's function in 2D and 3D. The derivation of reciprocal relations is presented for closed and open ducts. The adjoint equations are then solved numerically in reverse time by TDWP method. Reciprocity between the duct modes in the closed duct is derived and numerically validated. For the open duct, reciprocal relation between the duct mode amplitudes and far field point sources in the presence of the exhaust shear flow is derived and confirmed numerically. Applications of the adjoint problem to closed and open ducts are also presented.





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