Improved rocket propulsion directly translates to reduced fuel requirements and increased payloads for space flight. Rotating detonation rocket engines (RDREs) have the potential to provide significant performance gains in thrust-per-fuel ratio, design trade space, and mass savings compared to traditional rocket engines, and are attractive candidates for NASA lander, launch, and attitude-control applications. However, it is not currently known how to optimally design an RDRE injector, chamber, or nozzle to achieve what theory suggests is possible, so NASA needs capability for improved understanding of RDRE behavior. Because in situ diagnostics are limited and detailed computation is too computationally intensive for design iteration, I propose to develop a reduced-order computational model, capturing the important features of the flow, with emphasis on understanding the associated chaotic dynamics, for which no model currently exists. My model will run fast enough for use in design iteration and will be used to accelerate NASA’s ongoing RDRE development by quickly providing predictions for many design parameters. This improvement in evaluation turn-around time will allow for more detailed exploration of the design parameter space. In particular, I aim for this model to identify the geometric and operating parameters that determine the development of different wave modes in RDREs. Experiments have shown that current RDREs do not consistently exhibit the same wave modes and that different wave modes can produce different engine performance. Inconsistency in engine performance inhibits both practical use and efficient development of the technology, so the results of this work will inform optimal design practices and significantly advance NASA and industry development of RDREs. Thus, this work will enable the designs with the most favorable properties to be more quickly identified and iteratively refined to improve desired performance measures, directly supporting ongoing NASA development of next-generation RDRE design.