<p>Energetic materials (EMs) are multi-phase, multi-material mixtures in which reactive breakdown can occur with large heat release over short time scales. Eulerian frameworks for the simulation of compressible flow in heterogeneous EM must handle fast transients, and severe interfacial deformations that can occur as a shock wave traverse the material. The shock may also transition to a detonation wave, further exacerbating the complexity and challenges for simulation techniques. Previous simulation approaches have employed low-order numerical methods or diffuse interfaces to handle the high gradients and large material deformations. In this work, high-order numerical discretization and sharp interface treatments are combined to produce a high-fidelity modeling and simulation capability to accurately capture the reactive flow physics of EM at micro-, meso-, and macro-scales. Issues of stability and computational cost of the high-order scheme when implemented in concert with sharp interface treatments are addressed. The methodology is then applied to demonstrate the impact of high-accuracy simulations at the micro-scale: to calculate the hotspot ignition and growth due to the collapse of a micron-sized pore. Meso-scale simulations of shock-induced hotspot evolution in microstructures of neat-pressed (two-phase) EM show that the accuracy of the techniques significantly impacts the calculation of energy localization rates, which are used as closure models at the macro-scale. Finally, we show the ability of the methods to produce accurate simulations of macro-scale systems where shock-to-detonation transition occurs, requiring high accuracy in capturing the dynamics of curved detonation fronts interacting with embedded boundaries. This work establishes approaches toward solving a wide range of thermophysics problems that will be needed for the accurate design of systems operating on EM.</p>