Unexpected detonation of granular solid energetic materials is a key safety issue in the propellants manufacturing industry. In this work, a model developed for the characterization of the early stages of the detonation process of granular solid energetic materials is presented. The model relies on a two-phase approach which considers the conservation equations of mass, momentum, and energy and constitutive relations for mass generation, gas-solid particle interaction, interphase heat transfer, and particle-particle stress. The work considers an extension of approximated Riemann solvers and Total Variation Diminishing (TVD) schemes to the solid phase for the numerical integration of the problem. The results obtained with this model show a good agreement with data available in the literature and confirm the potential of the numerical schemes applied to this type of model. The results also permit to assess the effectiveness of different numerical schemes to predict the early stages of this transient combustion process.