The Pulse Detonation Engine consists of an initiation chamber and main combustion chamber. In the operation process, a deflagration is initiated in an initiation chamber filled with fuel-air mixture. Then, the deflagration rapidly transformed to detonation and finally, the detonation wave transition from the initiation chamber to the main combustion chamber. The combustor model used the same initial conditions with the pressure of 1atm and temperature of 300K. Hydrogen 2%and Air with Oxygen 22% are filled in the initiator and main combustor.In this paper, the flow fields of the PDE with a stoichiometric hydrogen-air mixture are numerically simulated. Effort is also expended to study the flow dynamics with low and high ignition energy in the initiation chamber, and the detonation wave propagation in main combustion chamber of PDE. The effects of shock wave propagation and reflection studied by fixing the dimensions of combustion chambers, initial conditions, outlet conditions and varying the pressure and temperature of ignition source of initiation chamber in single step and multi-steps reactions.At higher temperature and pressure, ignition is strong, or sharp. A single reaction center causes the abrupt appearance of a secondary shock induced by the explosive reaction. At lower temperature and pressure, the ignition is weak, or mild. The location of reaction centers where chemical reactions begin, appear behind the shock, and they gradually develop into an explosion.A high energy igniter can play an important role in rapid initiation techniques, but only as a means of initially creating a highly turbulent flame. The acceleration of that flame to detonation still consumes a considerable distance. The time of detonation depended on DDT length reduced, so that the ignition energy is very important for detonation process in the PDE combustion chamber.The multi-steps models are viewed as being more realistic than the traditional one-step models. The multi-step reaction models included initiation, branching, and termination steps. The situation with realistic combustion chemistry is more subtle and although chain termination alter the explosion time, peroxide chemistry may ultimately still enable an explosion to occur, compared the multi-steps model with traditional one-step models. The same condition of laminar to turbulent transition in these models, multi steps reaction model was necessary to used higher ignition energy than the single step model. In the model, the requirement of the lowest ignition energy caused to form detonation and the shock wave propagation difference between single step and multi-steps chemical reaction process were studied to provide a more convincible estimation of the propulsive performance of PDE. Under the initial condition of 1atm and 310K, the lowest ignition energy of initiator is obtained. This result will be useful in future designs of initiator for pulse detonation engines.