Water Quality Prediction in One-Dimensional Flow by Means of New Advective Transport Function and Convergence Criteria Modification

According to the low rainfall and the water resources in the country, investigation of the pollution behavior in water is very important. To Study on this phenomena, advection-diffusion equation in one-dimensional flow is used. Analytical solution and numerical solution can be used to solve this equation. The residual of numerical methods are decreased using computer simulation in recent years. Some researcher investigated a higher order numerical scheme for scalar transport. The computational principles of a numerical scheme for the solution of the two-dimensional scalar transport equation were presented in their study. They evaluated their model applicability in several examples involving tracer releases in to channel flows.
Some authors investigated on the modeling of solute transport using quick scheme. The scheme is shown to yield high accuracy in comparison with the more conventional second-order central-difference representation. A specified pollutant transport simulated in the river environments and compared with the numerical solutions. Hoffmann and Chiang as a part of their book entitled Computational Fluid Dynamics, discussed on the convergence constraints of the different numerical methods of pollution transport. He concluded that the maximum amount of this constraint is the state that the courant number is between 0 and 1. The objective of this research is to introduce the transport function that by maintaining positive characteristics of previous methods, modify existing divergence constraints.
In this paper a hypothetical case study in the real range is selected and is solved with different numerical solution like Lax, Fromm, Quick and etc. The analytical solution is chosen for the verification. The MAPLE software were used to do the computation of the new proposed advective transport function (Simple Exponential Function).
The results showed that the Quick method is shown the best agreement with the analytical solution and also the numerical solutions converge only when the courant number is less than 1. This makes constraints for the solution, time and distance interval selection. A new Simple exponential function in one dimensional pollutant transport of shallow water is proposed to eliminate this constraint. The calculated values of this new proposed function is in good agreement with the analytical and Quick method and also the courant number can be increase to 2 with the application of this function.
The new advective transport function entitled simple exponential function that proposed and presented in this investigation, is a suitable function for pollutant transport. This new advective transport function is in good agreement with the analytical and Quick method and also the courant number can be increase to 2 with the application of this function.