Modelagem matemática e métodos numéricos para a dispersão de poluentes: simulações em meios aquáticos e aéreos

Abstract

The growing environmental impact caused by human activities, stemming from industrialization and urbanization, along with the improper disposal of substances, necessitates enhancing the understanding of pollutant dispersion to mitigate their harmful effects on ecosystems. This undergraduate thesis aimed to study the behavior of pollutants in aquatic and aerial environments using mathematical modeling as a tool. For this purpose, the Partial Differential Equation of Advection-Diffusion and the Euler Equations were employed. The Advection-Diffusion Equation was numerically handled using the Finite Difference method, with a forward difference approximation for the temporal discretization, an Upwind scheme for the advective term, and a second-order centered approximation for the spatial discretization of the diffusive term. Meanwhile, the Euler Equations were discretized using the Lax-Friedrichs method, modified to account for numerical flux. Both models were implemented computationally using the Python programming language, and simulations were performed to analyze the pollutant’s behavior over time. It is expected that results from simulations like these can provide information for the creation of public policies and preventive measures aimed at mitigating the damage caused by pollutants, thereby contributing to environmental preservation.