The aerospace industry is a significant contributor to CO\(_2\) emissions, necessitating innovative propulsion technologies. Rotating detonation engines (RDEs) offer higher thermal efficiency than traditional deflagration combustion by utilizing detonation waves that travel azimuthally at speeds up to km/s. This study presents a three-dimensional numerical simulation of a premixed hydrogen-air RDE, achieving stable operation with a single detonation wave. The flowfield development from ignition to stable operation is analyzed, focusing on ignition phenomena, and comparing results with ideal Chapman-Jouguet (C–J) values. Challenges in modeling, such as computational resource limitations and achieving stable detonation, are addressed. The simulation successfully captured key flowfield structures, including detonation wave propagation, oblique shocks, and slip lines, with performance metrics (thrust: 940 N, specific impulse: 179 s) aligning with literature. A hydrogen-oxygen mixture failed to sustain stable detonation, highlighting the sensitivity of RDE operation and numerical models to fuel-oxidizer combinations. The study underscores the potential of RDEs for reducing fuel consumption (by up to 20% accordingly to literature) while improving efficiency, though challenges like backflow and injection modeling remain. These findings contribute to advancing RDE technology toward practical applications, supporting the development of environmentally friendly propulsion systems.