One-Dimensional Coupled Model of Surface Water Flow and Solute Transport for Basin Fertigation
Publication: Journal of Irrigation and Drainage Engineering
Volume 139, Issue 3
Abstract
A highly efficient and accurate numerical model of surface water flow and solute transport is useful in the design and evaluation of a basin fertigation system. In this study, a coupled model of surface water flow and solute transport for basin fertigation was first formulated. On the basis of the implicit–explicit time scheme of governing equation of the coupled model, the advection upstream splitting method (AUSM) and central finite-volume methods with scalar dissipation characteristic were employed to discretize the spatial derivatives of physical flux, spatial derivatives of advection matrix, diffusion vector, and water-level slope vector. The forming discretized algebraic equation group of the governing equation was solved in split technique, and a one-dimensional surface-flow and solute-transport coupled numerical model for basin fertigation was proposed. The ability of the proposed model was demonstrated using two numerical tests compared with the model on the basis of the Roe finite-volume method. Three field experiments were conducted to validate the proposed model. The results showed that the model exhibits excellent performance for determining water flow and solute transport under full-time, first-half, and second-half fertilizer-application experiments. The proposed model can serve as a research and practical tool for the design and management of basin fertigation.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This research was supported by the Projects of the National High-Tech R&D Program under Grant Nos. 2011AA100505 and 2011BAD25B04 and by the National Natural Science Foundation of China under Grant No. 51209227. The authors thank Li Fuxiang, Gao Zhanzhong, Dong Mengjun, and Liu Shanshan for their contributions to the field experiments. The authors are very grateful to the editors and reviewers for their comments and remarks, which have resulted in significant improvements to this manuscript.
References
Abbasi, F., et al. (2003). “Overland water flow and solute transport: model development and field-data analysis.” J. Irrig. Drain. Eng., 129(2), 71–81.
Bai, M., Xu, D., Li, Y., and Pereira, L. S. (2010). “Stochastic modeling of basins microtopography: Analysis of spatial variability and model testing.” Irrig. Sci., 28(2), 157–172.
Begnudelli, L., and Sanders, B. F. (2006). “Unstructured grid finite-volume algorithm for shallow-water flow and scalar transport with wetting and drying.” J. Hydraul. Eng., 132(4), 371–384.
Belov, A., Martinelli, L., and Jameson, A. (1995). “A new implicit algorithm with multigrid for unsteady incompressible flow calculations.” Proc., AIAA 33rd Aerospace Sciences Meeting and Exhibit, American Institute of Aeronautics and Astronautics, Reston, VA.
Boldt, A. L., Watts, D. G., Eisenhauer, D. E., and Schepers, J. S. (1994). “Simulation of water applied nitrogen distribution under surge irrigation.” Trans. ASAE, 37(4), 1157–1165.
Bradford, S. F., and Katopodes, N. D. (2001). “Finite volume model for non-level basin irrigation.” J. Irrig. Drain. Eng., 127(4), 216–223.
Bradford, S. F., and Sanders, B. F. (2002). “Finite-volume model for shallow-water flooding of arbitrary topography.” J. Hydraul. Eng., 128(3), 289–298.
Burgete, J., Garcia Navarro, P., and Murillo, J. (2008). “Preserving bounded and conservation solutions of transport in one-dimensional shallow-water flow with upwind numerical schemes: Application of fertigation and solute transport in rivers.” Int. J. Numer. Meth. Fluids, 56(9), 1731–1764.
Burguete, J., Zapata, N., García-Navarro, P., Maïkaka, M., Playán, E., and Murillo, J. (2009). “Fertigation in furrows and level furrow systems. I: Model description and numerical tests.” J. Irrig. Drain. Eng., 135(4), 401–412.
García-Navarro, P., Playán, E., and Zapata, N. (2000). “Solute transport modeling in overland flow applied to fertigation.” J. Irrig. Drain. Eng., 126(1), 33–40.
Hildebrand, F. B. (1974). Introduction to numerical analysis, McGraw-Hill, New York.
LeVeque, R. J. (2002). Finite volume methods for hyperbolic problems, Cambridge Univ., Cambridge, UK.
Li, Y. N. (1999). Basin irrigation in north China: Evaluation, modeling and design for improvement, Instituto Superior Agronomia, Lisbon, Portugal.
Liou, M. S. (1996). “A sequel to AUSM: .” J. Comput. Phys., 129(2), 364–382.
Liou, M. S., and Steffen, J. (1993). “A new flux splitting scheme.” J. Comput. Phys., 107(1), 23–39.
Murillo, J., Burguete, J., Brufau, P., and García-Navarro, P. (2005). “Coupling between shallow water and solute flow equations: Analysis and management of source terms in 2D.” Int. J. Numer. Meth. Fluids, 49(3), 267–299.
Playán, E., and Faci, J. M. (1997). “Border irrigation: Field experiment and a simple model.” Irrig. Sci., 17(4), 163–171.
Playán, E., Walker, W. R., and Merkley, G. P. (1994). “Two-dimensional simulation of basin irrigation. I: Theory.” J. Irrig. Drain. Eng., 120(5), 837–856.
Wang, X. P. (1997). “Nitrifying bacteria cultivation and aquaculture water study of ammonia nitrogen removal.” Master thesis, Wuxi Institute of Light Industry, Jiangsu province, China.
Xu, Z., and Shu, C. (2005). “Anti-diffusive flux correction for high order finite difference WENO schemes.” J. Comput. Phys., 205(2), 458–485.
Xu, Z., and Shu, C. (2006). “Anti-diffusive finite difference WENO methods for shallow water with transport of pollutant.” J. Comput. Math., 124(6), 239–251.
Zerihun, D., Furman, A., Warrick, A. W., and Sanchez, C. A. (2005a). “Coupled surface-subsurface solute transport model for irrigation borders and basins. I: Model development.” J. Irrig. Drain. Eng., 131(5), 396–406.
Zerihun, D., Sanchez, C. A., Furman, A., and Warrick, A. W. (2005b). “Coupled surface-subsurface solute transport model for irrigation borders and basins. II: Model evaluation.” J. Irrig. Drain. Eng., 131(5), 407–419.
Zhang, S., Xu, D., and Li, Y. (2012). “Two-dimensional numerical model of basin irrigation based on a hybrid numerical method.” J. Irrig. Drain. Eng., 138(9), 799–808.
Zhou, J. G., Causon, D. M., Mingham, C. G., and Ingram, D. M. (2001). “The surface gradient method for the treatment of source terms in the shallow-water equations.” J. Comput. Phys., 168(1), 1–25.
Information & Authors
Information
Published In
Journal of Irrigation and Drainage Engineering
Volume 139 • Issue 3 • March 2013
Pages: 181 - 192
Copyright
© 2013 American Society of Civil Engineers.
History
Received: May 16, 2011
Accepted: Sep 17, 2012
Published online: Sep 19, 2012
Published in print: Mar 1, 2013
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.