Numerical simulations of the spontaneous ignition and subsequent detonation of propane-air mixtures caused by a weak shock in a partially confined volume containing an obstacle are performed to study potential hazards from a leaking storage container. The numerical model combines a solution of the compressible equations of fluid dynamics with a phenomenological chemical induction model for species conversion and energy release. The purpose of the simulations is to study the mechanism of the ignition and detonation processes due to shock reflections from the wall boundaries. Nonreactive simulations show how the obstacle partially blocks the flow such that one portion of the shock front reflects off of the obstacle and another portion is transmitted. Reactive-flow simulations of stoichiometric propane-air show spontaneous ignition behind the shock reflected from the obstacle and later transition to detonation in the direction of the transmitted wave. A series of computations performed to study the effect of obstacle height show the various mechanisms responsible for the transition to detonation for the different obstacle sizes considered. Simulations in a mixture with variable stoichiometry around the obstacle, a more realistic picture of the physical scenario, show decay of the transmitted shock and then re-ignition as the shock reaches the stoichiometric region. Two separate areas of ignition eventually combine and transition to detonation. As this detonation propagates into the lean region far from the obstacle, it decays into a shock wave followed by a decaying flame front.