To shorten the ignition length of the wedge-induced oblique detonation wave, a geometric setup in which the leading and aft wedges are connected by a cavity is proposed. High-resolution viscous computations to solve the reactive Reynolds-averaged Navier-Stokes equations have been performed, which examine the onset and evolution of combustion and flow configuration with premixed mixtures of inflow Mach numbers ranging from 4.0 to 6.0. The unreactive flowfield of the cavity-based wedge is analogous to that of a sole cavity with the exclusion of shock/shock interaction downstream. For Ma=4.0 and 5.0, no sustainable oblique detonation wave is achieved, and the flame holds in the cavity and near-wall area of the aft wedge; however, a short-lived detonation wave triggered by the shock focuses is observed during the combustion procedure with Ma=5.0. For Ma=6.0, nearly direct detonation initiation of postshock occurs, and an oblique detonation wave is established above the fore edge of the cavity. Unexpectedly, a delayed ignition downstream contributes to the development of a recirculation zone, which results in a detached oblique detonation wave for Ma=5.5.