Progress in the analysis of the Forest Fire model.

Asymptotic analysis underlying Bdzil's Detonation Shock Dynamics (DSD) theory is used to obtain mesh-independent results for the Forest Fire burn model. Using the published burn rate for PBX 9501 as given by the Forest Fire model, and standard mixture rules for the products (pressure and temperature equilibrium), we obtain a D$_{n}-\kappa $ relation for PBX 9501. It provides a reasonable estimate for the failure diameter for PBX 9501. However, the deficit is extremely small even in the vicinity fo failure I.e., (D$_{CJ}$- D$_{n}$-)/D$_{CJ} \quad \sim $ O(10$^{-4})$, where D$_{CJ}$is the Chapman-Jouguet (CJ) detonation speed when compared to experimental results. It is pointed out that ameliorating the Forest Fire burn rate at pressures above 100 kbars leads to much improved results for the D$_{n}-\kappa $ curve.