<p>The one-dimensional model of pollution transport in shallow flows is investigated by numerically approximating it through the development and use of a well-balanced Runge–Kutta discontinuous Galerkin (RKGD) scheme. In order to accurately explain the flow of pollutant concentrations over varied bed surfaces, the advection dispersion equation, this model contains equations accounting for source terms and variable bottom topography. Third-order accuracy is obtained in the smooth case, and stability and accuracy are obtained by balancing flux and source gradients are guaranteed. Some physically significant test computations are presented to demonstrate the effectiveness and efficiency of the method. The reliability and accuracy of the scheme in the simulation of contaminant transport in shallow water are demonstrated by the applications. Our results confirm the reliability of the system and emphasize the potential of the present RKGD scheme as a useful tool for an accurate representation of pollutant transfer in shallow flows.</p>