A numerical computation of a non-dimensional form of stream water quality model with hydrodynamic advection–dispersion–reaction equations

Mathematical models of water quality assessment problems often arise in environmental science. The modelling often involves numerical methods to solve the equations. In this research, two mathematical models are used to simulate pollution due to sewage effluent in the nonuniform flow of water in a stream with varied current velocity. The first is a hydrodynamic model that provides the velocity field and elevation of the water flow. The second is a dispersion model, where the commonly used governing factor is the one-dimensional advection–dispersion–reaction equation that gives the pollutant concentration fields. In the simulation processes, we used the Crank–Nicolson method system of a hydrodynamic model and the backward time central space scheme for the dispersion model. Finally, we present a numerical simulation that confirms the results of the techniques.