An analytical technique is reported for the simple and accurate calculation of the trajectory of the leading edge of a free or driven blast wave in a uniform or nonuniform medium of arbitrary geometry and such related quantities as shock velocity and the temperature at the edge. An expression for the overall energy balance of a spherical blast is obtained which can be used as a simple differential equation for determining the shock position and velocity in terms of a constant. The accuracy of the technique is demonstrated, and it is shown how the results obtained form the basis for evaluating radiative processes in a shocked plasma, such as a supernova remnant, as well as their temporal evolution.
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Cavaliere et al. (1976) studied this question.