We have developed a continuum modeling approach, grounded in classical physical chemistry, based on the following assumptions that the thermodynamic states in the material can be represented by local stationary averages of the pressure (stress), temperature, and mass fractions computed from atomistic simulation, and that the mixture has well-defined molecular components, each with a complete equation of state. The continuum model,”The Gibbs formulation”, applies to near-atomic length and time scales, which we identify as the scales where the highest 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 CVE simulations of a constant volume thermal explosions of RDX were performed using reactive molecular dynamics (RMD), that used ReaxFF to 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. Joshi and Chaudhuri used RMD to simulate a sustained spatially distributed deflagration in a nano-scale slab of HMX; Journal of Physical Chemistry C, 122, 14434-14446, (2018). Those RMD results are binned for macroscopic properties using the CV formulation by spatially averaging 20 bins. Mirrored continuum simulations considered only two components, reactant and product. 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.