when a nuclear explosive is fired or a laser fusion pellet is imploded, radiation energy becomes a significant portion of the total energy and account must be taken of it. The diffusion approximation has proven to be a useful means of incorporating radiation physics in codes of this type. The three principal problems associated with the finite difference solution of the diffusion equation are the conservation of energy, the spatial differencing on grids that are becoming distorted with the passage of time, and the coupling of calculations done on the separate regional grids that together constitute the geometry of the problem. The difference techniques described are applied to the calculation of the prompt effects of an explosive detonated at the earth's surface. The explosive and the region of the earth more than 3 m from the explosive were zoned with Lagrangian coordinates. The air, the earth directly under the explosive, and a distant sink region were zoned in Eulerian coordinates. The calculation was carried out until most of the energy of the explosive was converted into kinetic energy and thermal energy in the air and earth.