In the present work a sixth-order hybrid WENO–Centered Difference (CD) scheme with an adaptive mesh refinement method is employed to investigate gaseous detonation by injecting a hot jet into a hydrogen–oxygen combustible mixture flowing at supersonic speed. Two-dimensional reactive Navier–Stokes (NS) equations with one-step two-species chemistry model are solved numerically. The comparison between viscous and inviscid detonation structures shows that due to the absence of both the physical viscosity in Euler equations and minimization of numerical dissipation in the hybrid WENO–CD scheme, very small-scale vortices can be observed behind the detonation front. The diffusion effect in the NS equations suppresses the small-scale vortices, but it has negligible influence on the large-scale vortices generated by Richtmyer–Meshkov (RM) instability and those along the highly unstable shear layers induced by Kelvin–Helmholtz (KH) instability. When studying the same setup in an expanding channel and beyond the point of detonation initiation, it is found that because of the diffusion effect of detached shear layers, any unburned jet flow is consumed quickly and then additional energy is released periodically. Because of the formation of multiple secondary triple points and subsequent shear layers after the shutdown of the hot jet, a highly turbulent flow is produced behind the detonation front. Rather than the commonly known RM instability, the large-scale vortices involved in the highly unstable shear layers dominate the formation of the turbulent flow and the rapid turbulent mixing between the unburned jet flow and burned product. It is found that the size of unburned jets and vortices due to KH instability is growing for larger expansion angles. The further generated turbulent flow resulting from larger sized vortices, significantly enhances the mixing rate behind the Mach stem, leading to rapid consumption of the unburned reactants. Therefore, detonations propagate faster in channels with larger expansion angle and higher expansion ratio.