Simulating Condensational Growth, Evaporation, and Coagulation of Aerosols Using a Combined Moving and Stationary Size Grid

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Abstract
We present a numerical method of simulating the aerosol processes of coagulation, condensational growth, and evaporation over a hybrid size grid. In the hybrid grid, the volume of involatile core material is constant for each size bin, but the volume of volatile material fluctuates. Since particles in each bin grow and evaporate at their own pace, particles from one bin can obtain the same volume as those from another bin while maintaining different composition. Similarly, particles from different bins that grow to the same size can evaporate back to their respective original core sizes. Allowing independent growth of particles inhibits numerical diffusion since particles in each bin grow or evaporate to their actual sizes. When two particles coagulate, they form a new particle with core volume between the core volumes of particles in two other bins. We partition the new particle and its total volume between these two bins. Similarly, we adapt other processes, such as nucleation, emissions, and transport to the hybrid grid structure. The condensational growth equations developed conserve mass between the gas phase and size-distributed aerosol phase. Because the equations result in sparse matrices of partial derivatives, SMVGEAR, a sparse-matrix Gear-type integrator, solves them quickly. Furthermore, the semi-implicit coagulation equations used here conserve volume exactly, are absolutely stable, and require no iteration. Finally, we compared model solutions to both analytical and other integrated numerical solutions. To obtain numerical solutions, we developed and integrated equations that simulate simultaneous coagulation and growth of multicomponent particles.