Future large-scale particle accelerators, for example, the Future Circular Collider (FCC), the Compact Linear Collider (CLIC) and the International Linear Collider (ILC), will require significant RF drive power on the order of 100 MW. Thus, an RF source with high efficiency is preferable to minimise the overall power required. Klystrons represent an attractive RF source, with the current state of the art operating at efficiencies of up to 70%. Such devices feature monotonic bunching, where at the output cavity, a number of electrons will not be in the main bunch, and instead will be present in the anti-bunch, and therefore not contributing to the output power. Therefore, novel bunching methods, such as the Core Oscillation Method (COM), are worthy of investigation. By allowing the core of the electron beam to bunch and de-bunch between successive cavities, the number of electrons contained in the final bunch can increase, and therefore improve the efficiency of the device. Numerical simulation of klystrons featuring COM will be presented, with efficiencies of up to 85% being predicted thus far.