DUAL RECIPROCITY BOUNDARY ELEMENT METHOD FOR SOLVING TIME-DEPENDENT WATER INFILTRATION PROBLEMS IN IMPERMEABLE CHANNEL IRRIGATION SYSTEMS

  • Yanne Irene Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah Jakarta, Indonesia https://orcid.org/0000-0002-1513-0583
  • Muhammad Manaqib Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah Jakarta, Indonesia https://orcid.org/0000-0002-5439-5867
  • Mochammad Rafli Alamsyah Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah Jakarta, Indonesia https://orcid.org/0009-0006-4137-3315
  • Madona Yunita Wijaya Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah Jakarta, Indonesia https://orcid.org/0000-0001-9142-7197
DOI: https://doi.org/10.30598/barekengvol19iss4pp2583-2596
Keywords: DRBEM, Furrow Irrigation, Modified Helmholtz Equation, Water infiltration;

Abstract

The mathematical model of water infiltration in a furrow irrigation channel with an impermeable layer in homogeneous soil is formulated as a Boundary Value Problem (BVP) with the Modified Helmholtz Equation as the governing equation and mixed boundary conditions. The purpose of this study is to solve the infiltration problem using the Dual Reciprocity Boundary Element Method (DRBEM). The results show that the highest values of suction potential and water content are located beneath the permeable channel, while the lowest values are found at the soil surface outside the channel and beneath the impermeable layer. The values of suction potential and water content increase over time t and converge, indicating stability in the infiltration process. These findings align well with real-world scenarios, demonstrating that the developed mathematical model and its numerical solution using DRBEM accurately illustrate the time-dependent water infiltration process in impermeable furrow irrigation channels.

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References

A. K. Sari, “ANALISIS KEBUTUHAN AIR IRIGASI UNTUK LAHAN PERSAWAHAN DUSUN TO’ PONGO DESA AWO GADING KECAMATAN LAMASI,” PENA TEKNIK: Jurnal Ilmiah Ilmu-ilmu Teknik, vol. 4, no. 1, pp. 47–51, 2019.doi: https://doi.org/10.51557/pt_jiit.v4i1.214

C. Yang, C. Liu, Z. Qiu, S. Wang, X. Xing, and X. Ma, “MULTI-OBJECTIVE IRRIGATION STRATEGIES AND PRODUCTION PREDICTION FOR WINTER WHEAT IN CHINA IN FUTURE DRY YEARS USING CERES-WHEAT MODEL AND NON-DOMINATED SORTING GENETIC ALGORITHM II,” Comput Electron Agric, vol. 230, 2025, doi: https://doi.org/10.1016/j.compag.2024.109888.

M. G. Bos, WATER REQUIREMENTS FOR IRRIGATION AND THE ENVIRONMENT. New York: Springer, 2008. [Online]. Available: www.iwmi.cgiar.org

M. Burton, IRRIGATION MANAGEMENT PRINCIPLES AND PRACTICES. Wallingford: CAB International, 2010.doi: https://doi.org/10.1079/9781845935160.0000

M. Manaqib, “PEMODELAN MATEMATIKA INFILTRASI AIR PADA SALURAN IRIGASI ALUR,” Jurnal Matematika “MANTIK,” vol. 3, no. 1, p. 25, 2017, doi: https://doi.org/10.15642/mantik.2017.3.1.25-31.

W. Ang, A BEGINNER’S COURSE IN BOUNDARY ELEMENT METHODS. Florida: Universal Publiser, 2007.

N. Yulian Ashar and I. Solekhudin, “A NUMERICAL STUDY OF STEADY POLLUTANT SPREAD IN WATER FROM A POINT SOURCE,” Engineering Letters, vol. 29, no. 3, pp. 1–9, 2021.

C. Pozrikidis, A PRACTICAL GUIDE TO BOUNDARY ELEMENT METHODS WITH THE SOFTWARE LIBRARY BEMLIB. Washington, D.C.: A CRC Press Company, 2003.doi: https://doi.org/10.1201/9781420035254

I. Solekhudin and K. C. Ang, “A DUAL-RECIPROCITY BOUNDARY ELEMENT METHOD FOR STEADY INFILTRATION PROBLEMS,” ANZIAM Journal, vol. 54, no. 3, pp. 171–180, Jan. 2013, doi: https://doi.org/10.1017/S1446181113000187.

J. T. Katsikadelis, BOUNDARY ELEMENTS THEORY AND APPLICATIONS. Athen: Elsevier Science Ltd. All, 2002.doi: https://doi.org/10.1016/B978-008044107-8/50006-7

A. Nurhasanah, M. Manaqib, and I. Fauziah, “ANALYSIS INFILTRATION WATERS IN VARIOUS FORMS OF IRRIGATION CHANNELS BY USING DUAL RECIPROCITY BOUNDARY ELEMENT METHOD,” Jurnal Matematika “MANTIK,” vol. 6, no. 1, pp. 52–65, 2020, doi: https://doi.org/10.15642/mantik.2020.6.1.52-65.

S. Inna, M. Manaqib, V. D. Samudra, and R. Erhandi, “AN ANALYSIS OF INFILTRATION IN FURROW IRRIGATION CHANNELS WITH ROOT WATER UPTAKE,” J Appl Math, vol. 2024, 2024, doi: https://doi.org/10.1155/2024/1869349.

I. Solekhudin, “A NUMERICAL METHOD FOR TIME-DEPENDENT INFILTRATION FROM PERIODIC TRAPEZOIDAL CHANNELS WITH DIFFERENT TYPES OF ROOT-WATER UPTAKE.,” IAENG International Journal of Applied Mathematics, vol. 48, no. 1, 2018.doi: https://doi.org/10.2991/icomse-17.2018.6

I. Solekhudin, “TIME-DEPENDENT INFILTRATION FROM PERIODIC SEMI-CIRCULAR CHANNELS WITH TWO DIFFERENT TYPES OF ROOT-WATER UPTAKE,” in 1st Annual International Conference on Mathematics, Science, and Education (ICoMSE 2017), Atlantis Press, 2017, pp. 26–30.doi: https://doi.org/10.2991/icomse-17.2018.6

A. A. Beyene and S. Eslamian, “DITCH AND FURROW IRRIGATION,” in Handbook of Irrigation Hydrology and Management: Irrigation Methods, 2023, pp. 51–63. doi: https://doi.org/10.1201/9780429290152-6.

J. Yu et al., “THE EFFECT OF PLUG HEIGHT AND INFLOW RATE ON WATER FLOW CHARACTERISTICS IN FURROW IRRIGATION,” Agronomy, vol. 12, no. 9, 2022, doi: https://doi.org/10.3390/agronomy12092225.

M. Kilic, “MINIMIZATION OF DEEP PERCOLATION BY A PARABOLIC SIMULATION MODEL IN A BLOCKED END FURROW IRRIGATION METHOD,” Irrigation and Drainage, vol. 71, no. 5, pp. 1195–1207, 2022, doi: https://doi.org/10.1002/ird.2724.

I. Solekhudin and A. Zulijanto, “A NUMERICAL STUDY OF STEADY INFILTRATION FROM A SINGLE IRRIGATION CHANNEL WITH AN IMPERMEABLE SOIL LAYER,” 2017.

Y. Irene, M. Manaqib, V. W. Ramadhanty, and A. R. Affriani, “AN ANALYSIS OF WATER INFILTRATION IN FURROW IRRIGATION CHANNELS WITH PLANTS IN VARIOUS TYPES OF SOIL IN THE SPECIAL REGION OF YOGYAKARTA USING DUAL RECIPROCITY BOUNDARY ELEMENT METHOD,” JTAM (Jurnal Teori dan Aplikasi Matematika), vol. 8, no. 3, pp. 780–799, 2024.doi: https://doi.org/10.31764/jtam.v8i3.19873

I. Solekhudin and K. C. Ang, “SUCTION POTENTIAL AND WATER ABSORPTION FROM PERIODIC CHANNELS IN DIFFERENT TYPES OF HOMOGENEOUS SOILS,” Electronic Journal of Boundary Elements, vol. 10, no. 2, Jun. 2012, doi: https://doi.org/10.14713/ejbe.v10i2.1760.

M. Manaqib, “PENYELESAIAN MASALAH SYARAT BATAS DUAL RECIPROCITY BOUNDARY ELEMENT METHOD,” no. 2, pp. 115–132, 2018.

N. Inayah, M. Manaqib, and W. N. Majid, “FURROW IRRIGATION INFILTRATION IN VARIOUS SOIL TYPES USING DUAL RECIPROCITY BOUNDARY ELEMENT METHOD,” in AIP Conference Proceedings, 2021. doi: https://doi.org/10.1063/5.0042682.

A. Amoozegar‐Fard, A. W. Warrick, and D. O. Lomen, “DESIGN NOMOGRAPHS FOR TRICKLE IRRIGATION SYSTEMS,” Journal of Irrigation and Drainage Engineering, vol. 110, no. 2, pp. 107–120, Jun. 1984, doi: https://doi.org/10.1061/(ASCE)0733-9437(1984)110:2(107).

A. W. Warrick, Soil physics companion. CRC press, 2001.

I. Solekhudin and K.-C. Ang, “A DRBEM WITH A PREDICTOR–CORRECTOR SCHEME FOR STEADY INFILTRATION FROM PERIODIC CHANNELS WITH ROOT-WATER UPTAKE,” Eng Anal Bound Elem, vol. 36, no. 8, pp. 1199–1204, 2012, doi: https://doi.org/10.1016/j.enganabound.2012.02.013.

Published
2025-09-01
How to Cite
[1]
Y. Irene, M. Manaqib, M. R. Alamsyah, and M. Y. Wijaya, “DUAL RECIPROCITY BOUNDARY ELEMENT METHOD FOR SOLVING TIME-DEPENDENT WATER INFILTRATION PROBLEMS IN IMPERMEABLE CHANNEL IRRIGATION SYSTEMS”, BAREKENG: J. Math. & App., vol. 19, no. 4, pp. 2583-2596, Sep. 2025.
Issue
Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Section
Articles

Copyright (c) 2025 Yanne Irene, Muhammad Manaqib, Mochammad Rafli Alamsyah, Madona Yunita Wijaya

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