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

Document Type : Complete scientific research article

Authors

1 Assistant Professor, Dept. of Civil Engineering, Faculty of Engineering, University of Sistan and Baluchestan, Zahedan, Iran,

2 M.Sc. Student, Dept. of Civil Engineering, Faculty of Engineering, University of Sistan and Baluchestan, Zahedan

3 Assistant Professor, Dept. of Civil Engineering, Faculty of Engineering, University of Sistan and Baluchestan, Zahedan,

4 Associate Professor, Dept. of Civil Engineering, Faculty of Engineering, University of Sistan and Baluchestan, Zahedan

Abstract

Abstract
Background and objectives: 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.
Materials and Methods: 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).
Results: 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.
Conclusion: 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.

Keywords

References

1.Abbot, M.B., and Basco, D.R. 1997. Computational Fluid Dynamics: An Introduction for Engineers. Longman Singapore Publisher (Pte) Ltd, 425p.
2.Ardestani, M., Sabahi, M.S., and Montazeri, H. 2015. Finite Analytic Methods for Simulation of Advection- Dominated and Pure Advection Solute Transport With Reaction in Porous Media. Int. J. Environ. Res. 9: 1. 197-204.
3.Barry, D.A., and Sposito, G. 1989. Analytical solution to a convection-dispersion model timedependent transport coefficients. Water Resour Research. 25: 12. 2407-2416.
4.Falconer, R.A., and Liu, S. 1988. Modeling solute transport using quick scheme. J. Environ. Engin. ASCE. 114: 1. 22160.
5.Glass, J., and Rodi, W. 1982. A higher order numerical scheme for scalar transport. Computer Methods in Applied Mechanics and Engineering. 31: 337-358.
6.Hoffmann, K.A., and Chiang, S.T. 2000. Computational Fluid Dynamics. A Publication of Engineering System, Wichita, Kansas, 67208-1078, USA, 208p.
7.Kamphuis, J.W. 1991. Physical Modeling. I in Handbook of Coastal and Ocean Engineering . Vol2, Gulf Publishing Company, Houston Texas.
8.Kim, K.C., Park, G.H., Jung, S.H., Lee, J.L., and Suh, K.S. 2011. Analysis on the characteristics of a pollutant dispersion in river environment. Annals of Nuclear Energy.
38: 232-237.
9.Kumar, A., Jaiswal, D., and Kumar, N. 2009. Analytical solutions of one-dimensional advection-disperion equation with variable coefficients in a fnite domain. J. Earth Syst. Sci. 118: 5. 539-549.
10.Li, S., and Duffy, C.J. 2012. Fully-coupled modeling of shallow water flow and pollutant transport on unstructured grids. Environmental Sciences. 13: 2098-2121.
11.Schmalle, G.F., and Rehmann, C.R. 2014 Analytical solution of a model of contaminant transport in the advective zone of a river. J. Hydraul. Eng. ASCE 7900.0000885. (1-8).
12.Singh, P., Yadav, S.K., and Kumar, N. 2012. One-Dimensional pollutant’s advective- diffusive transport from a varying pulse-type point source through a medium of linear heterogeneity. J. Hydrol. Engin. 17: 9. 1047-1052.
13.Van Genuchten, M.Th., and Alves, W.J. 1982. Analytical solutions of the one-dimensional convective-dispersive solute transport equation. U.S. Department of Agriculture. Technical Bulletin. No. 1661. 151.
14.Yadav, R.R., Jaiswal, D.K., and Yadav, H.K. 2010. Analytical solution of one dimensional temporally dependent advection-dispersion equation in homogeneous porous media. Inter. J. Engin. Sci. Technol. 2: 141-148.
15.Yoshioka, H., and Unami, K. 2013. A cell-vertex finite volume scheme for solute transport equations in open channel networks. Probabilist. Eng. Mech. 31: 30-38.
16.Zheng, N.S. 1996. Mathematical Modeling of Groundwater pollution, Springer.
17.Zoppou, C., and Knight, J.H. 1997. Analytical solution for advection and advection-dispersion equation with spatially variable coefficient. J. Hydr. Engin. 123: 2. 144-148.
Journal of Water and Soil Conservation
Volume 23, Issue 2
June 2016
Pages 147-162

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