Numerical solution of pollutant transport model with source term by RDTM

Abstract

The focus of this paper is the study of mathematical model for the analysis of diffusion and transport processes of chemicals in river systems. In the present study, we have introduced a one-dimensional model that is described by time-dependent convection-diffusion differential equations. The focus of our study is the potential pollution of the river, both with and without a specific pollution source. The current investigation aims to analyze the impact of two different input source functions, namely constant and linear forms.   In order to validate the model, we conducted a study on the diffusion and transport of chemicals, specifically focusing on NO$_3$ and PO$_4$ of the Tapi river.  Reduced differential transform method (RDTM) is used to obtain solutions. For the accuracy of the solution, the convergence of solution function is examined in each case obtained from RDTM. The pollutant concentration at various distances and time levels has been shown numerically and graphically in each case. The pollution levels with and without sources are compared in 2D and 3D graphs. The methodology proposed in this study for river pollution prediction using a 1D pollution model can be applied to other rivers.