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A 1-Dimensional (1-D) model of fluid dynamic and chemistry kinetics following hot spot auto-ignition has been developed to simulate the process from auto-ignition to pressure wave propagation. The role of wall effect on the physical-chemical interaction process is numerically studied. A pressure wave is generated after hot spot auto-ignition and gradually damped as it propagates. The reflection of the wall forms a reflected pressure wave with twice the amplitude of the incident wave near the wall. The superposition of the reflected and forward pressure waves reinforces the intensity of the initial pressure wave. Wall effect is determined by the distance between the hot spot center and the cylinder wall. Hot spot auto-ignition near the wall easily initiates detonation under high-temperature and high-pressure conditions because pressure wave reflection couples with chemical reactions and propagates in the mixture with high reactivity.