Detonation of the flow of a combustible mixture over a wedged channel is numerically simulated. A two-dimensional, time accurate, finite-volume-based method is used to perform the computations, and a five-species, two-step chemical reaction is assumed for a stoichiometric hydrogen-air mixture. The combustion channel is made of a wedged section followed by a constant area section. The simulation was performed with wedges of up to 20 deg semi-angle and Mach numbers from 2 to 6.5, with other inflow parameters fixed. Different types of flows arise depending on the wedge angle and the incoming Mach number. Propagating and standing detonation waves modes were found, both of which can be further subdivided, depending on where the detonation is initiated. Moreover, a case without combustion was discovered for a narrow range of Mach numbers for the 5 deg wedge.