A good understanding of the physical properties of explosives is essential for their safe and efficient usage. Numerical simulations have proven to be an excellent tool with which to develop and verify models which describe both ignition and detonation of explosives.

The objective of this work is to improve the robustness and accuracy of numerical simulations of both ideal and non-ideal explosives. Much of the complexity of the detonation phenomenon arises due to the finite width of the reaction zone, which causes the properties of the detonation wave to deviate from the predictions of the ZND model. If numerical models are to predict the attributes of the explosive to greater accuracy, then the dynamics of the reaction zone must be adequately resolved. This thesis also reviews the scientific literature in order to contextualise the developments presented here.

The approach taken in this thesis is to describe the thermodynamics in the reaction zone as a mixture of reactants and products which exist at pressure and thermal equilibrium. To this end, mechanical equations of state of Mie-Gr"{u}neisen form are developed with extensions, which allow the temperature to be evaluated appropriately, and the temperature equilibrium condition to be applied robustly. Furthermore the snow plow model is used to capture the effect of porosity.

The methodology is applied to predict the velocity of compliantly confined detonation waves. Once reaction rates are calibrated for unconfined detonation velocities, simulations of confined rate sticks and slabs are performed, and the experimental detonation velocities are matched without further parameter alteration, demonstrating the predictive capability of our simulations. We apply the same methodology to both the non-ideal explosive EM120D (an ANE or ammonium nitrate based emulsion) and the comparatively ideal TATB based explosive PBX 9502. Furthermore, this thesis presents a novel methodology to use gauge data from shock initiation experiments to calculate values for the reaction rate. The methodology can be applied to determine rate law parameters without the use of computationally intensive hydrocode simulations. The validity and limitations of this approach are demonstrated through its application to simulated gauge data for an idealized explosive. The resulting rate law is then used in simulations of shock to detonation transition, and confined detonation waves of the TATB based explosive PBX 9502. Comparison of the results with experimental data is favourable.