Two-dimensional computations of the propagation of a detonation in a low-pressure, argon-diluted mixture of hydrogen and oxygen were performed using a detailed chemical reaction mechanism. Cellular structure developed after an initial perturbation was applied to a one-dimensional solution placed on a two-dimensional grid. The energy-release pattern in a detonation cell showed that, in addition to the primary release of energy behind the Mach stem, there is a secondary energy release that starts about two-thirds of the way through the cell. Reignition, which occurs as transverse waves collide, results in an explosion that spreads over a region and releases a considerable amount of energy. Resolution tests showed convergence of the detonation mode (number of triple points or transverse waves) reached at the end of the computations, as well as global and local energy release. The computations were performed on massively parallel Connection Machines for which new approaches were developed to maximize the speed and efficiency of integrations.