We have developed a continuum modeling approach, grounded in classical physical chemistry, based on the following assumptions: (1) that the states in the material can be represented by local stationary averages of the pressure (stress), temperature, and mass fractions computed from atomistic simulation, (2) and that the mixture has well-defined molecular components, each with a complete equation of state. The continuum model, "Gibbs formulation", applies to near-atomic length and time scales, which we identify as the scales where the high frequency, high energy phonons equilibrate in molecular mixtures, (about six atomic radii and six to ten vibrational periods). Phase changes and chemical changes due to reaction are not in (asymptotically, long-time) equilibrium, and changes are assumed to occur on much longer time scales than those required for stress and temperature equilibration. Recently in the Journal of Chemical Physics, J. Chem. Phys. 144, 184111 (2016), we carried out both atomistic molecular dynamics (MD) simulations and "mirrored" continuum simulations to model, thermal ignition of a nano-sized cube of explosive RDX. The NVE ensemble simulations of a constant volume explosions of RDX were performed using reactive molecular dynamics (RMD), that use ReaxFF as model chemical changes in the MD simulation. The MD simulation was regarded as the exact molecular system. The continuum simulation was regarded as an interpretation and measurement of the average chemical changes between a set of identified chemical components of that molecular system. In this work, we extend these ideas to include spatial averaging to study wave propagation and spatially distributed transport, combined with chemical reaction and compare continuum based simulations with recent RMD simulations of a sustained spatially distributed deflagration in a nano-scale slab of HMX carried out by Joshi and Chaudhuri, similarly done in RDX. [3] Both atomistic and continuum simulations show a hot spot ignition followed by a structured deflagration that propagates through the HMX slab and are compared with good to excellent agreement. (C) 2020 The Combustion Institute. Published by Elsevier Inc. All rights reserved.