Similarity Analysis of the Radiative Gas Dynamic Equations with Spherical Symmetry

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Abstract
Similarity representation of the radiative gas dynamic equations with spherical symmetry, amenable to a wide variety of radiation law, is presented. The general representation of the equations of motion is effected by the simple artifice of retaining the definitions of the radiant quantities as operators on the radiative intensity and of recognizing the variability of the index refraction. Specific constitutive forms for the radiation field manifest themselves in implied constraint conditions. Because of radiative heating, similarity structure may be prescribed for the gas on both sides of shock waves. Numerical examples are constructed for strong explosions and implosions.

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