Introducing a new method for calculating the spatial and temporal distribution of pollutants in rivers

Abstract

Using constant coefficients is an inefficient way to explain the details of the problem of pollutant transport. This is due to factors such as nonuniform geometry, discharge changes, flow velocity and dispersion coefficient variations. Previous studies indicate that the ratio of studies on pollutant transport in rivers is lower than those on the porous media. However, the relative complexity of the solution of the pollutant transport equation in rivers (especially in the case of variable coefficients) in comparison with porous media highlights the importance of focusing on the solutions for rivers environment. In this study, the one-dimensional equation of pollutant transport in the river with location-dependent variables (velocity, dispersion coefficient and cross-section area) with arbitrary pattern is solved via the generalized integral transform technique (GITT) in a finite-length domain and general initial and boundary conditions. In this study, the results obtained from the presented analytical solution are compared to those obtained from the existing analytical solutions in previous studies for the two states of constant and variable coefficients. To further test the accuracy of this method, we have compared the results obtained from the presented analytical solution with the results obtained from numerical solution based on finite-difference method by applying the conditions of two real rivers. Comparison of the results of the GITT verification with available analytical solutions as well as numerical solutions shows the high accuracy and the applicability of the proposed solution considering arbitrary patterns of the ADRE coefficients and general initial and boundary conditions.