Improved analytical and numerical techniques for calculating explosions and implosions

Theoretical investigations in connection with the hypervelocity launcher research efforts carried on at the Fluid Dynamics Facilities Research Laboratory have required a detailed study of strong explosions and implosions. 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, y, 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. On the other hand, the numerical approach is time-consuming and also results in inaccuracies in the vicinity of the center. As a means of circumventing the above difficulties, the exact analytical solutions have been cast into a form which permits an iterative determination of all of the physical quantities directly as functions of position.