Many processes in the atmosphere begin highly localized, but eventually grow to large-scale events. Stratospheric aerosol injection is one such process, involving a number of multiscale, highly non-linear phenomena that strongly influence the long-time evolution of an aerosol seeding event. Accurate simulation of this type of process challenges state-of-the-art models and numerical methods in a number of ways: scalar fields describing chemistry and aerosols must be transported with minimal numerical diffusion at resolutions far-below the Earth-scale Eulerian mesh resolution; consistent and conservative transport of sub-grid-scale scalar fields is required to preserve the time-temperature history of evolving chemistry and aerosols; and computations must be affordable and scalable. We propose applying the Eulerian-Lagrangian Point-Mass Particle (ELPMP) method to the modeling and simulation of localized atmospheric chemistry and aerosol processes as a solution to these challenges. The ELPMP method is a new modeling and simulation scheme comprised of simultaneous Eulerian and Lagrangian discretizations of the same realization of a flow system. It provides consistent and conservative transport in the presence of material discontinuities without Lagrangian remeshing by virtue of a novel relationship between the point mass-particle velocity and the fluid particle velocity. All advection is performed via transport of Lagrangian particles, allowing for long-time evolution of the sub-grid-scale aerosol physics and chemistry. In this talk, we describe the application of the ELPMP to the modeling of atmospheric chemistry and aerosol dynamics, and demonstrate the evolution of an aerosol system at scales representative of a stratospheric aerosol injection event. Results suggest the ELPMP to be a valuable technique for simulating atmospheric chemistry and aerosols.