Modeling solute transport in rivers: Analytical and numerical solutions

Abstract

This study presents a novel analytical framework for modeling one-dimensional solute transport in rivers, integrating advection, rate-limited adsorption on suspended sediments, and first-order degradation. Analytical solutions are used to validate the numerical scheme’s accuracy under idealized conditions, tested for instantaneous and continuous pollutant discharges. The research importantly investigates short-term solute accumulation in riverbeds, a critical yet understudied process that affects sediment transport and pollutant fate. Applicable to a wide range of contaminants (e.g., nutrients, pesticides), the framework aids water quality assessment, pollution control, and risk mitigation. Implemented in the open-source SWASHES library, these solutions provide practical tools for decision-support systems and serve as reliable benchmarks to validate numerical models. By addressing transient and persistent pollutant scenarios, this work enhances predictive capabilities for environmental management. The approach bridges analytical and numerical methods, offering a robust foundation for simulating solute transport across industrial and ecological contexts, advancing sustainable water resource management.