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Published: 1978

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A diffusion equation modeling the flow of radiation was added to the hydrodynamic equations of two coupled Eulerian and Lagrangian finite-difference computer codes. This addition permits the extension of the range of problems to which these codes may be applied to include those in which temperatures on the order of a thousand electron volts are attained. The coupled codes are first-order-accurate shock hydrodynamics programs designed to calculate transient effects resulting from concentrations of high energy density. Such phenomena occur when a projectile impacts a target or when a high explosive is detonated. When the energy density is very high, as 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.