Dealing accurately with the material interfaces in this problem is a long-standing challenge, as familiar strategies lead to spurious temperature spikes, and therefore spurious reaction rate spikes. We describe a new strategy, which does not generate spurious spikes, and demonstrate via a number of test problems that numerical convergence can be achieved. We also examine two problems that are stepping stones to a complete simulation; both are planar. In the first, we consider the passage of a shock wave through pure HMX in which a line of hot spots of the kind generated by void collapse are located a short distance behind the shock. When the hot spot spacing is large, the shock remains a shock; when small, transition to detonation occurs. In the second problem we also insert hot spots, but into a matrix of HMX particles and binder.