Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Aeronautics and Astronautics

First Advisor

Paul I. King, PhD


A new adaptive split-domain harmonic balance computational fluid dynamics (CFD) method is developed to solve highly nonlinear time-periodic flows such as those found in turbomachinery. The basic harmonic balance CFD method transforms an unsteady time-periodic problem into a steady-state problem by assuming a solution in the form of a Fourier series in time. The new method employs a unique multi-domain split-operator solution technique to remove a large-series stability restriction present in previous harmonic balance CFD approaches. In addition, the new method adapts the frequency content to the flow, starting with a small number of Fourier frequencies and augmenting the frequency content in each cell as necessary to capture local flow physics. The method reduces compute times by allowing larger integration time steps, eliminating Fourier transforms, and reducing overall problem size. The stability and accuracy of the method are verified with solutions to the 1-D inviscid Burger's equation and 1-D Euler's equation. Accurate adapted quasi-1-D Euler solutions for a supersonic/subsonic diverging nozzle with periodic unsteady outflow conditions are generated in 86% less time than an equivalent non-adapted split-domain solution, demonstrating the performance benefit of matching frequency content to the local flow conditions.

AFIT Designator


DTIC Accession Number