The numerical procedure for the burning of Ammonium Perchlorate (AP) with a Fuel-Binder
(Hydroxyl Terminated Polybutadience HTPB) is presented. This model accounts for the two-steps
reaction mechanism for the primary diffusion flame between the decomposition products of the
Binder (B) and the oxidizer AP and the primary premixed AP flame. Moreover, this current model
allowed for the complete coupling between the gas-phase physics, the condensed-phase physics,
and the unsteady non-uniform regression of the propellant surface. The parameters used in this
model are fitted to experimental data for the combustion of APVHTPB. The propagation of the
unsteady non-planer regression surface is described, using the Essentially-Non-Oscillatory (ENO)
scheme with the aid of the level set strategy. The Alternating-Direction-Implicit (ADI) solver is
employed to solve the full Navier-Stokes equations in the gas phase for the variable density model.
The results show the effect of various parameters on the surface propagation speed, flame
structure, and the burning surface geomew. A comparison between the computational and
experimental results is presented.