Dimensional Splitting Finite-Volume Method for Two-Dimensional Surface Water Flow Model in Basin Irrigation
Publication: Journal of Irrigation and Drainage Engineering
Volume 140, Issue 4
Abstract
The concept of major direction correction is proposed, which includes complete major direction correction, major direction correction without roughness, and no major direction correction, based on the dimensional splitting expression of a two-dimensional surface water flow model in surface irrigation. The dimensional splitting finite-volume methods for basin irrigation were developed based on the major direction correction and existing dimensional splitting numerical methods, in addition to the scalar dissipation finite-volume method. The simulation performance of two-dimensional surface water flow models of basin irrigation constructed by the dimensional splitting finite-volume methods were comparatively validated and analyzed based on basin irrigation experiments. The results show that the models based on the Strang dimensional splitting methods with complete major direction correction and major direction correction without roughness have similar simulation accuracy and convergence rates with the model based on the dimensional nonsplitting finite-volume method. By comparison, the models based on the Strang dimensional splitting methods with no major direction correction and major direction correction without roughness exhibit better water conservation ability and computational efficiency than the model based on the dimensional nonsplitting finite-volume method. Consequently, the Strang dimensional splitting method with major direction correction without roughness can be used as a numerical method in the development of two-dimensional surface water flow models for basin irrigation.
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 by the National Natural Science Foundation of China under Grant No. 51209227, 51279225. We are very grateful to the senior programmer Song Chaoda and Dr. Du Weifu for their help in debugging simulation code.
References
Bautista, E., Clemens, A. J., Strelkoff, T. S., and Schlegel, J. (2009). “Modern analysis of surface irrigation systems with WinSRFR.” Agric. Water Manage., 96(7), 1146–1154.
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., 371–384.
Begnudelli, L., and Sanders, B. F. (2007). “Conservative wetting and drying methodology for quadrilateral grid finite-volume models.” J. Hydraul. Eng., 312–322.
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., 289–298.
Bradford, S. F., and Sanders, B. F. (2005). “Performance of high-resolution, nonlevel bed, shallow-water models.” J. Eng. Mech., 1073–1081.
Brufau, P., Garcia, N. P., Playán, E., and Zapata, N. (2002). “Numerical modeling of basin irrigation with an upwind scheme.” J. Irrig. Drain. Eng., 212–223.
LeVeque, R. J. (2002). Finite volume methods for hyperbolic problems, Cambridge University Press, Cambridge, England.
Li, Y. N. (1999). Basin irrigation in north China: Evaluation, modeling and design for improvement, ISA, Lisbon.
Liou, M. S. (1996). “A sequel to AUSM: AUSM+.” J. Comput. Phys., 129(2), 364–382.
Liou, M. S., and Steffen, C. J., Jr. (1993). “A new flux splitting scheme.” J. Comput. Phys., 107(1), 23–39.
Playán, E., Walker, W. R., and Merkley, G. P. (1994). “Two-dimensional simulation of basin irrigation, I: Theory.” J. Irrig. Drain. Eng., 837–856.
Sanders, B. F., and Brandford, S. F. (2006). “Impact of limiters on accuracy of high-resolution flow and transport models.” J. Eng. Mech., 87–98.
Shao, S., and Lo, E. Y. M. (2003). “Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface.” Adv. Water Resour., 26(7), 787–800.
Strelkoff, T. S., Tamimi, A. H., and Clemmens, A. J. (2003). “Two-dimensional basin flow with irregular bottom configuration.” J. Irrig. Drain. Eng., 391–401.
Tan, W. (1992). Shallow water hydrodynamics, Elsevier-Water and Power Press, Beijing, China.
U.S. Arid-Land Agricultural Research Center (2006). WinSRFR 1.0 user manual (draft), USALARC, Maricopa, AZ.
Vico, G., and Porporato, A. (2011). “From rainfed agriculture to stress-avoidance irrigation: I. A generalized irrigation scheme with stochastic soil moisture.” Adv. Water Resour., 34(2), 263–271.
Vivekanand, S., and Bhallamudi, M. S. (1997). “Hydrodynamic modeling of basin irrigation.” J. Irrig. Drain. Eng., 123(6), 407–414.
Zhang, S., Xu, D., Li, Y., and Bai, M. J. (2012). “A two-dimensional numerical model of basin irrigation based on a hybrid numerical method.” J. Irrig. Drain. Eng., 799–808.
Zhang, S., Xu, D., Li, Y., and Bai, M. J. (2013). “One-dimensional coupled model of surface water flow and solute transport for basin fertigation.” J. Irrig. Drain. Eng., 181–192.
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 140 • Issue 4 • April 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Jun 7, 2013
Accepted: Nov 26, 2013
Published online: Jan 6, 2014
Published in print: Apr 1, 2014
Discussion open until: Jun 6, 2014
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.