A Numerical Framework for Pollutant Transport in Shallow-Water Flows: Application to the Niger River in Bamako

We propose a unified numerical framework for the transport of passive pollutants by shallow-water flows. The mathematical model we consider for describing this phenomenon results in the coupling of the hydrodynamic shallow-water equations with a two-dimensional advection–diffusion equation governing the pollutant transport. The numerical implementation of this hyperbolic model, based on the finite element method, is achieved using a multiphysics modeling and simulation toolbox featured by Feel++, a versatile C++ library applying the Galerkin methods for solving partial differential equations. Numerical experiments targeted on arsenic, cadmium, and lead, heavy metals among the most harmful to human health, are presented as part of a practical application on the Niger River in Bamako. The framework is validated on the basis of RMSE and MAE metrics, some of the most commonly used error measures in linear regression, using observational data. These indicators, estimated below 5% of the observed mean value, support the reliability and accuracy of the numerical model in capturing pollutant dynamics under flow conditions. The simulation results highlight the predictive effectiveness of this framework and provide better insight into pollution patterns in the scrutinized river section.