Fast Numerical Methods for the Propagation of Blast Waves Produced by Finite Spherical Charges

Geometrical shock dynamics (GSD), first introduced by Whitham, is a much faster model than the hydrodynamic model for simulating shock propagation, and uses shock surface geometry to determine velocity and acceleration. However the propagation of air shocks from explosions, predicted by Taylor's theory (and others), is very different from GSD model predictions, even if both start with the same position and velocity. The main reason is that the uniform flow Whitham assumed for GSD is not applicable to the sharply attenuating gas flow behind the air blast wave. Therefore, we have developed a new model for blast waves in the GSD framework that can apply both to Taylor blast theory and blast waves that can be produced from finite explosions. The scaling law embedded in the Mach number and radius (M-R) relation for spherical blast wave theory is the general principle we use in the new model. We have used CTH simulations to validate the scaling law for an ideal explosive (PBX9501) and for a non-ideal explosive (TNT). The M-R relation obtained from the CTH simulations and that by our fast model appeared to be essentially identical, which validates a new model for blast waves in the air.