Improved Analytical and Numerical Techniques for Calculating Explosions and Implosions,
AEROSPACE RESEARCH LABS WRIGHT-PATTERSON AFB OH
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Theoretical investigations in connection with the hypervelocity launcher research efforts have required a detailed study of strong explosions and implosions. For some time, it has been known that the system of partial differential equations defining pressure, density, and particle velocity can be converted to a system of ordinary differential equations by means of a similarity transformation. In the case of an exploding blast wave, the similarity transformation can be explicitly determined by consideration of the principle of energy conservation. The resulting system of equations which ultimately contains only one parameter, namely the adiabatic constant, gamma, can then be integrated numerically, using the known relations at the shock front as initial conditions. Alternatively, known analytic solutions are available, but these have not been used extensively since they are implicit and do not allow the direct determination of the desired physical quantities pressure, density, and velocity at a given point.