A commercially available computational fluid dynamics code was used to study the unsteady thrust augmentation of a complete pulsejet/ejector system. A 50 cm long pulsejet was used as a driving source. Combined systems, consisting of the pulsejet and ejectors with different geometries, were simulated. Computed, limit-cycle thrust augmentation values compared favorably to experimentally obtained values for the same setups. The starting vortex generated by the pulsejet and its interaction with the ejector was investigated in detail. Results suggest that the optimal diameter of the ejector is related to its position, decided by the path of the vortex ring. The effect of the length of the ejector was also investigated and showed to have a minor effect and related to the acoustic process.