Propagation and stability of diverging cylindrical detonation in hydrogen air mixture is numerically simulated and the mechanism of the transverse waves is analysed. For the numerical modelling, anew solver based on compressible, transient, reactive Navier Stokes equations is developed which can the simulate detonation propagation and extinction in hydrogen-air mixture. A single step reaction mechanism is tuned to ensure the detonation and deflagration properties (in case of detonation failure) can be simulated accurately. The solver is used for modelling various detonation scenarios, in particular cylindrical diverging-detonations, because most of accidental industrial detonations start from a spark and then a diverging-detonation propagates outwards. The diverging-detonation, its cellular structure and adoption with the increased surface area at the detonation front, as well as interactions with obstacles leading to detonation failure and re-initiation are studied.subse