Book excerpt: The results of some numerical calculations of the impact of steel cylinders and spheres on the plastic-bonded high explosive PBX 9501 are described. The calculations were carried out by a reactive, multicomponent, two-dimensional, Eulerian hydrodynamic computer code, 2DE. The 2DE computer code is a finite difference code that uses the donor-acceptor-cell method to compute mixed cell fluxes. The mechanism of shock initiation to detonation in heterogeneous explosives is best described as local decomposition at hot spots that are formed by shock interactions with density discontinuities. The liberated energy strengthens the shock so that as it interacts with additional inhomogeneities, hotter hot spots are formed, and more of the explosive is decomposed. The shock wave grows stronger until a detonation begins. This mechanism of initiation has been described numerically by the Forest Fire burn model, which gives the rate of explosive decomposition as a function of local pressure. The parameters in the Forest Fire burn model have been developed from experiments where the induced shock approximates a plane wave and are applied, in this case, to a situation where the induced shock is a divergent wave with curvature that depends on the size and shape of the projectile. The calculated results have been compared with results from experiments involving instrumented mock and live high explosives, with projectiles of varying sizes, shapes, and velocities. We find that there is good agreement between the calculated and experimental data.