Numerical routing of tracer concentrations in rivers with stagnant zones

Modeling pollution transmission in rivers is an important subject in environmental engineering studies. Numerical approaches to modeling pollution transmission in rivers are useful tools for managing the water quality. The advection-dispersion equation is the governing equation in the transport of pollution in rivers. Recently, due to advances in fractional calculus in engineering modeling, the simulation of pollution transmission in rivers has been improved using the fractional derivative approach. In this study, by solving the fractional advection-dispersion equation (FRADE), a numerical model was developed for the simulation of pollution transmission in rivers with stagnant zones. To this purpose, both terms of the FRADE equation (advection and fractional dispersion) were discretized separately and the results were connected using a time-splitting technique. The analytical solution of a modified advection-dispersion equation (MADE) model and observed data from the Severn River in the UK were used to demonstrate the model capabilities. Results indicated that there is a good agreement between observed data, the analytical solution of the MADE model, and the results of the developed numerical model. The developed numerical model can accurately simulate the long-tailed dispersion processes in a natural river.