AbstractA physical and mathematical model, computational algorithms, and calculation results are presented for the ignition and detonation of methane–air combustible mixtures behind a reflected shock wave. The one-dimensional, unsteady equations of gas dynamics, supplemented with the equations of chemical kinetics, are solved numerically with the grid-characteristic and Godunov methods. An original modification of the simplified kinetic mechanism is used to describe the combustion of methane in air. The results of calculations of the ignition delay time of the combustible mixture are compared with the experimental and calculated data reported by other authors, and the results of calculations of the occurrence and propagation of the detonation wave are presented. The modes of the propagation of a detonation wave with a constant velocity and in oscillatory mode are obtained. The velocity of the detonation wave in the absence of oscillations accurately corresponds to the velocity of the overcompressed detonation wave obtained from the solution of the Rankine–Hugoniot equations under the assumption that the flow is frozen in front of the shock wave and equilibrial behind the shock wave and that the gas velocity behind the shock wave is zero.