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The problem of detonation attenuation in stoichiometric methane-oxygen and its re-establishment following its interaction with obstacles was investigated using high resolution numerical simulation. The main focus was on the role of the transverse detonation on the re-establishment of the detonation wave. We applied an efficient thermochemically derived four-step global combustion model using an Euler simulation framework to investigate the critical regimes present. While past attempts at using one- or two- step models have failed to capture transverse detonations, for this scenario, our simulations have demonstrated that the four-step combustion model is able to capture this feature. We suggest that to correctly model detonation re-initiation in characteristically unstable mixtures, an applied combustion model should contain at least an adequate description to permit the correct ignition and state variable response when changes in temperature and pressure occur. Our simulations reveal that there is a relationship between the critical outcomes possible and the mixture cell size, and while pockets of unburned gas may exist when a detonation re-initiates, it is not the direct rapid consumption of these pockets that gives rise to transverse detonations. Instead, the transverse detonations are initiated through pressure amplification of reaction zones at burned/unburned gas interfaces whose combustion rates have been enhanced through Richmyer-Meshkov instabilities associated with the passing of transverse shock waves, or by spontaneous ignition of hot spots, which can form into detonations through the Zel'dovich gradient mechanism. In both situations, non-uniform ignition delay times are found to play a role. Finally, we found that the transverse detonations are in fact Chapman-Jouguet detonations, but whose presence contributes to overdriving the re-initiated detonation along the Mach stem.