Simulating advance distance in border irrigation systems based on the improved method of characteristics
Keywords:
border irrigation, numerical solution, advance distance, method of characteristicsAbstract
Improving the simulation accuracy of the advance distance based on the method of characteristics is essential to develop numerical solutions for simulating surface irrigation. Instead of volume balance in the traditional method of characteristics (T-MC), the position of critical flow is determined to simulate the advance distance in the improved method of characteristics (I-MC), which is used in border irrigation systems with rapid variation in inflow discharge in the current research. Specifically, the zones of both subcritical and supercritical flow were firstly distinguished to determine the position of the critical flow point, which was also the upstream boundary of the wetting front region, and then the advance distance was calculated by applying the diffusive wave equation in the wetting front region. The results showed that the I-MC accurately simulated the advance distance with high determination coefficients (0.984-0.998) and low errors (root mean square error of 0.35-1.56 min and coefficient of residual mass of 0.01-0.06), which performed much better than the T-MC. The I-MC provided a suitable and simple numerical simulation tool to improve the establishment of numerical surface irrigation models. Keywords: border irrigation, numerical solution, advance distance, method of characteristics DOI: 10.25165/j.ijabe.20211403.5877 Citation: Liu K H, Jiao X Y, Guo W H, Salahou M K, Gu Z. Simulating advance distance in border irrigation systems based on the improved method of characteristics. Int J Agric & Biol Eng, 2021; 14(3): 156–162.References
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[31] Sayari S, Rahimpour M, Zounemat-Kermani M. Numerical modeling based on a finite element method for simulation of flow in furrow irrigation. Paddy and Water Environment, 2017; 15(4): 879–887.
[32] Liu K, Jiao X, Liu Y. Inversion method of border flow rate based on water balance principle. China Rural Water and Hydropower, 2016; 8: 102–104. (in Chinese)
[33] Akbari M, Gheysari M, Mostafazadeh-Fard B, Shayannejad M. Surface irrigation simulation-optimization model based on meta-heuristic algorithms. Agric Water Manage, 2018; 201: 46–57.
[34] Li J, Zhu T, Mao X, Adeloye A J. Modeling crop water consumption and water productivity in the middle reaches of Heihe River Basin. Computers and Electronics in Agriculture, 2016; 123: 242–255.
[35] Bautista E, Strelkoff T S, Clemmens A J. Errors in infiltration calculations in volume-balance models. J Irrig Drain Eng, 2012; 138(8): 727–735.
[36] Douglas J, Russell T F. Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures. Siam Journal on Numerical Analysis, 1982; 19(5): 871–885.
[37] Zhang S, Xu D, Li Y, Wei Z. Review on simulation study of surface flow and solute transport for basin fertigation. Journal of Irrigation and Drainage, 2011; 30(3): 124–128. (in Chinese)
[38] Ebrahimian H, Keshavarz M R, Playán E. Surface fertigation: A review, gaps and needs. Spanish Journal of Agricultural Research, 2014; 12(3): 820–837.
[2] Lam Y, Slaughter D, Wallender W W, Upadhyaya S K. Computer vision system for automatic control of precision furrow irrigation system. In: Proceedings of 2006 ASAE Annual Meeting, 2006; Paper number 062078. doi: 10.13031/2013.20693.
[3] Valipour M. Comparison of surface irrigation simulation models: full hydrodynamic, zero inertia, kinematic wave. Journal of Agricultural Science, 2012; 4(12): 68–74.
[4] Valipour M, Sefidkouhi M A G, Eslamian S. Surface irrigation simulation models: A review. International Journal of Hydrology Science and Technology, 2015; 5(1): 51–70.
[5] McClymont D. Development of a decision support system for furrow and border irrigation. Doctoral dissertation. Toowoomba: University of Southern Queensland, Australia, 2007; 337p.
[6] García-Navarro P, Playán E, Zapata N. Solute transport modeling in overland flow applied to fertigation. Journal of Irrigation and Drainage Engineering, 2000; 126(1): 33–40.
[7] LeVeque R J. Finite volume methods for hyperbolic problems. London: Cambridge University Press, 2002; 578p.
[8] Walkley M, Berzins M. A finite element method for the two-dimensional extended Boussinesq equations. International Journal for Numerical Methods in Fluids, 2002; 39(10): 865–885.
[9] Zhang S, Xu D, Li Y. A one-dimensional complete hydrodynamic model of border irrigation based on a hybrid numerical method. Irrigation Science, 2011; 29(2): 93–102.
[10] Zarmehi F, Tavakoli A. A simple scheme to solve Saint-Venant equations by finite element method. International Journal of Computational Methods, 2016; 13(1): 1650001. doi: 10.1142/S0219876216500018.
[11] Eslami M R, Hetnarski R B, Ignaczak J, Noda N, Sumi N, Tanigawa Y. The method of characteristics. In: Theory of elasticity and thermal stresses. Springer, 2013; 810p.
[12] Barros R M, Tiago Filho G L, dos Santos I F S, da Silva F G B. Case studies for solving the Saint-Venant equations using the method of characteristics: Pipeline hydraulic transients and discharge propagation. Proceedings of the 27th IAHR Symposium on Hydraulic Machinery and Systems (IAHR 2014); Montreal, Canada: IOP Publishing Ltd., 2015; pp.55–62.
[13] Afshar M, Rohani M, Taheri R. Simulation of transient flow in pipeline systems due to load rejection and load acceptance by hydroelectric power plants. International Journal of Mechanical Sciences, 2010; 52(1): 103–115.
[14] Rao C K, Eswaran K. Pressure transients in incompressible fluid pipeline networks. Nuclear Engineering and Design, 1999; 188(1): 1–11.
[15] Katrašnik T. Improved model to determine turbine and compressor boundary conditions with the method of characteristics. International Journal of Mechanical Sciences, 2006; 48(5): 504–516.
[16] Singh V, Bhallamudi S M. Complete hydrodynamic border-strip irrigation model. J Irrig Drain Eng., 1996; 122(4): 189–197.
[17] Afshar M, Rohani M. Water hammer simulation by implicit method of characteristic. International Journal of Pressure Vessels and Piping, 2008; 85(12): 851–859.
[18] Strelkoff T. Algebraic computation of flow in border irrigation. Journal of the Irrigation and Drainage Division, 1997; 103(3): 357–377.
[19] Esfandiari M, Maheshwari B. Field values of the shape factor for estimating surface storage in furrows on a clay soil. Irrigation Science, 1997; 17(4): 157–161.
[20] Valiantzas J D. Volume balance irrigation advance equation: variation of surface shape factor. J Irrig Drain Eng, 1998; 123(4): 307–312.
[21] Bautista E, Strelkoff T, Clemmens A. Improved surface volume estimates for surface irrigation volume-balance calculations. J Irrig Drain Eng, 2012; 138(8): 715–726.
[22] Lalehzari R, Nasab S B. Improved volume balance using upstream flow depth for advance time estimation. Agric Water Manage, 2017; 186: 120–126.
[23] Salahou M K, Jiao X, Lü H. Border irrigation performance with distance-based cut-off. Agric Water Manage, 2018; 201: 27–37.
[24] Liu Y, Hui S. Mathematical model and a numerical method for the flow in border irrigation. Journal of Hydraulic Engineering, 1987; 2: 3–12. (in Chinese)
[25] Su L, Wang Q, Shan Y, Zhou B. Estimating soil saturated hydraulic conductivity using the Kostiakov and Philip infiltration equations. Soil
Sct Soc Am J, 2016; 80(6): 1463–1475.
[26] Kincaid D C, Heermann D F, Kruse E G. Hydrodynamics of border irrigation advance. Transactions of the ASAE, 1972; 15(4): 674–680.
[27] Whitham G B. The effects of hydraulic resistance in the dam–break problem. Proc Roy Soc of London, 1955; 227(1170): 399–407.
[28] Chanson H. Application of the method of characteristics to the dam break wave problem. J Hydraul Res, 2009; 47(1): 41–49.
[29] Liem R, Köngeter J. Application of high-speed digital image processing to experiments on dam break waves. Proc CADAM Meeting, Zaragossa, Spain, 1999; pp.399–411.
[30] Bautista E, Clemmens A J, Strelkoff T S, Schlegel J. Modern analysis of surface irrigation systems with WinSRFR. Agric Water Manage, 2009; 96(7): 1146–1154.
[31] Sayari S, Rahimpour M, Zounemat-Kermani M. Numerical modeling based on a finite element method for simulation of flow in furrow irrigation. Paddy and Water Environment, 2017; 15(4): 879–887.
[32] Liu K, Jiao X, Liu Y. Inversion method of border flow rate based on water balance principle. China Rural Water and Hydropower, 2016; 8: 102–104. (in Chinese)
[33] Akbari M, Gheysari M, Mostafazadeh-Fard B, Shayannejad M. Surface irrigation simulation-optimization model based on meta-heuristic algorithms. Agric Water Manage, 2018; 201: 46–57.
[34] Li J, Zhu T, Mao X, Adeloye A J. Modeling crop water consumption and water productivity in the middle reaches of Heihe River Basin. Computers and Electronics in Agriculture, 2016; 123: 242–255.
[35] Bautista E, Strelkoff T S, Clemmens A J. Errors in infiltration calculations in volume-balance models. J Irrig Drain Eng, 2012; 138(8): 727–735.
[36] Douglas J, Russell T F. Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures. Siam Journal on Numerical Analysis, 1982; 19(5): 871–885.
[37] Zhang S, Xu D, Li Y, Wei Z. Review on simulation study of surface flow and solute transport for basin fertigation. Journal of Irrigation and Drainage, 2011; 30(3): 124–128. (in Chinese)
[38] Ebrahimian H, Keshavarz M R, Playán E. Surface fertigation: A review, gaps and needs. Spanish Journal of Agricultural Research, 2014; 12(3): 820–837.
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Published
2021-06-11
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Liu, K., Jiao, X., Guo, W., Salahou, M. K., & Gu, Z. (2021). Simulating advance distance in border irrigation systems based on the improved method of characteristics. International Journal of Agricultural and Biological Engineering, 14(3), 156–162. Retrieved from https://ijabe.migration.pkpps03.publicknowledgeproject.org/index.php/ijabe/article/view/5877
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