Simulating advance distance in border irrigation systems based on the improved method of characteristics

Kaihua Liu,Zhe Gu,Mohamed Khaled Salahou,Xiyun Jiao,Weihua Guo

doi:10.25165/j.ijabe.20211403.5877

Abstract

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.

Highlights

Surface irrigation is the most common method for irrigating farmland across the world
Finite difference method is relatively intuitive[5], it leads to numerical vibrations in the flow front region[6]
The finite element method and the finite volume method, which divide the computational domain into irregular units, are advantageous in solving two-dimensional flow calculations with complex boundary conditions and wide water surface[7,8], while the procedure of computations is complex[9,10]

Summary

Introduction

Surface irrigation is the most common method for irrigating farmland across the world. Numerical analysis methods are critical tools for evaluating and simulating the surface flow of irrigation systems. The complete hydrodynamic model, known as the Saint-Venant equations, is the most comprehensive and accurate one for simulating surface irrigation[3]. Saint-Venant equations, the hyperbolic partial differential equations, can be derived through numerical solutions, such as the finite difference method, the method of characteristics, the finite element method and the finite volume method. The finite element method and the finite volume method, which divide the computational domain into irregular units, are advantageous in solving two-dimensional flow calculations with complex boundary conditions and wide water surface[7,8], while the procedure of computations is complex[9,10]

Methods

Results

Conclusion