MATHEMATICAL MODELING, ANALYSIS AND NUMERICAL SIMULATION OF AIR QUALITY USING THE ADVECTION-DIFFUSION-REACTION EQUATION

In this thesis, we study an air quality model by using a nonlinear one-dimensional advection-diffusion-reaction system of partial differential equations for NO-NO2-O3 chemical cycle. The model incorporates advection, diffusion, chemical reactions, and source terms, and is formulated based on standard atmospheric chemistry. We first develop numerical methods to approximate the solutions of the governing equations. Both explicit and implicit finite difference schemes are considered, and the implicit scheme provides approximations without any restrictions on the stability. The model is then nondimensionalized to identify key parameter combinations governing the system. This leads us to a regime in which the transport and source terms dominate the qualitative behavior of the solution. An important analysis is also performed to study invariant regions and boundedness, where we ensure that the solutions remain nonnegative and physically meaningful. An approximate steady-state solution is obtained using a regular perturbation method. We observe a strong agreement between analytical and numerical solutions, indicating that the approximation captures the long-term behavior of the system in the weak reaction regime. Finally, we use sensitivity analysis to investigate the influence of key parameters, particularly the reaction rate and photolysis rate. The results show that the system behaves in a predictable way in response to parameter changes, and the sensitivity-based approximations provide plausible estimates of perturbed solutions. Overall, this work provides an understanding of the interaction between transport and chemical processes in atmospheric pollution models.