Mathematical modeling of air pollution dynamics

Air quality models are used to explain pollution formation in urban and global regions. The chemically reactive flows that govern pollution dynamics and transformations are represented by a large formidable set of stiff, non-linear partial differential equations. Due to the large and stiff set of equations, numerical techniques are used to obtain solutions. This dissertation addresses the development of competitive numerical solutions of chemical transport models and the analysis of aerosol formation through numerical techniques.; The decoupling of operators using operator splitting produces a set of dynamical systems. These include advection, diffusion, chemistry, aerosol condensation/evaporation, deposition, and emissions. The most challenging operators to solve are advection and aerosol condensation/evaporation due to their hyperbolic nature. In light of their difficulty two new numerical schemes are developed: (1) The first is a new numerical algorithm for advection using quintic splines: QSTSE (Quintic Spline Taylor Series Expansion). QSTSE is an Eulerian flux based scheme that uses quintic splines to compute space derivatives and Taylor series expansion to march in time. (2) The second is a new method developed to solve the condensation equation as it relates to Air Quality Models using both semi-Lagrangian and Lagrangian fluxes to increase resolution and perform accurately under stringent conditions that occur in the atmosphere. The new method, Partitioned Flux Integrated Semi-Lagrangian Method (PFISLM), can be used with lower-order interpolators and it produce highly accurate results.; In the past, the coupled dynamics are not calculated due to their computational burden. In this research, a non-splitting (coupled) technique is developed to analyze the performance of operator splitting techniques in air quality models. The non-splitting method developed achieves convergence by reducing time steps, adapting timesteps to insure convergence, and eliminating operator splitting.; The final objective of this research is the analysis of pollution control and its effects on aerosol formation. The qualitative and quantitative behavior of aerosol dynamics resulting from the control of reducing nitrogen oxides (NO_x) and Volatile Organic Compounds (VOC) emissions is analyzed in this research by calculating detailed pollutant isopleths. (Abstract shortened by UMI.)...