Mathematical modelling in river pollution control

Abstract

This study is conducted to determine the concentration of coliform bacteria along a river. Coliform bacteria are used as the indicator for the pollution level of a river because its concentration in wastewater discharges is much more compared to the concentration of other microorganisms. A mathematical model based on the convection reaction equation will be developed to determine the concentration of coliform bacteria along a river. Before studying the convection reaction equation, we will study the solutions of the simpler model based on the linear advection equation. The model based on the linear advection equation will be solved analytically using the method of characteristics. The model will also be solved numerically using the first order upwind scheme. The graphical outputs for the solution of the model will be presented using MATLAB. After analysing the linear advection equation, we will move on to the convection reaction equation. This equation will be solved analytically using the method of variable change and integrating factor. Once the equation is solved, the solution is plotted using Maple for an easier analysis of the result. The result suggests that the concentration of coliform bacteria is the highest at the source of wastewater discharges.