Numerical Simulation of Pollutant Transport in the Rio das Mortes Using Finite Element Methods

This study investigates pollutant dispersion in the Rio das Mortes using mathematical modeling based on partial differential equations. The research applies the Finite Element Method (FEM) for spatial discretization and the Crank-Nicolson method for temporal discretization. The Navier-Stokes equation is used to model the river's velocity field, providing a realistic representation of pollutant transport. The study focuses on a specific region in Nova Xavantina, Mato Grosso, where agricultural activities, mining, and tributary streams influence water quality. Two different pollution scenarios are analyzed: (1) a single upstream pollutant source, and (2) multiple pollutant sources, including tributary inputs. The numerical simulations indicate that in the first scenario, pollutant concentration stabilizes after approximately six days, while in the second scenario, stability is reached after 125 days. The results highlight the effectiveness of mathematical modeling in predicting environmental impacts and aiding in pollution management. However, the lack of field data limits the precision of the simulations. Future work should include field sampling to calibrate the model parameters and validate the results. Additionally, developing a computational tool to simulate different pollution scenarios in riverine environments could be beneficial for environmental policy-making. This research underscores the importance of mathematical and computational tools in ecological studies, contributing to sustainable water resource management.