Hamilton, Mark F.2016-01-262018-01-222016-01-262018-01-222006-12http://hdl.handle.net/2152/32843The goal of this research project is to develop a method for examining the frequency components present a thermoacoustic device based upon perturbation analysis. This paper documents the evolution of the linear thermoacoustic solver developed in 1960s by Nicholas Rott to a higher order approximation of the thermoacoustic equations by the author. The method will be carried out to third order to provide a means to compute the nonlinear corrections to the fundamental mode. The method developed will utilize symmetries in the computational region to reduce the required solution to a one-dimensional problem along the axis of the resonator. The result of this project is a description of the method employed, the development of a tool for numerically computing the higher order terms in the perturbation scheme, and the impact of the perturbation terms on the output of the thermoacoustic device.electronicengCopyright © is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.Frequency componentsThermoacoustic devicePerturbation analysisThesisRestricted