This document details original numerical studies performed by the author pertaining to the propellant oxidizer, ammonium perchlorate (AP). Detailed kinetic mechanisms have been utilized to model the combustion of the monopropellants AP and ADN, and a two-dimensional diffusion flame model has been developed to examine the flame structure above an AP/HTPB composite propellant. This work was part of an ongoing effort to develop theoretically based, a priori combustion models. The improved numerical model for AP combustion utilizes a “universal” gas-phase kinetic mechanism previously applied to combustion models of HMX, RDX, GAP, GAP/RDX, GAP/HMX, NG, BTTN, TMETN, GAP/BTTN, and GAP/RDX/BTTN. The universal kinetic mechanism has been expanded to include chlorine reactions, thus allowing the numerical modeling of AP. This is seen as a further step in developing a gas-phase kinetic mechanism capable of modeling various practical propellants. The new universal kinetic mechanism consists of 106 species and 611 reactions. Numerical results using this new mechanism provide excellent agreement with AP's burning rate, temperature sensitivity, and final species data. An extensive literature review has been conducted to extract experimental data and qualitative theories concerning ADN combustion. Based on the literature review, the first numerical model has also been developed for ADN that links the condensed and gas phases. The ADN model accurately predicts burning rates, temperature and species profiles, and other combustion characteristics of ADN at pressures below 20 atm. Proposed future work and modifications to the present model are suggested to account for ADN's unstable combustion at pressures between 20 and 100 atm. A two-dimensional model has been developed to study diffusion in composite propellant flames utilizing a vorticity formulation of the transport equations. This formulation allows for a more stable, robust, accurate, and faster solution method compared to the Navier-Stokes formulations of the equations. The model uses a detailed gas-phase kinetic mechanism consisting of 37 species and 127 reactions. Numerical studies have been performed to examine particle size, pressure, and formulation effects on the flame structure above an AP/HTPB propellant. The modeled flame structure was found to be qualitatively similar to the BDP model. Results were consistent with experimental observations. Three different combustion zones, based on particle size and pressure, were predicted: the AP monopropellant limit, the diffusion flame, and a premixed limit. Mechanistic insights are given into AP's unique combustion properties.