Abstract
We present a solution to the problem of the induction of an adiabatic explosion by a shock of arbitrary dynamics. We obtain a general expression for the induction time as a function of the velocity, acceleration and total curvature of the shock. We derive a necessary condition for explosion that ensures bounded values of the induction time. The method is illustrated by determining conditions for initiation by impact of a piston, and it is validated by means of direct numerical simulations.
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