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Study on the detection of groundwater boundary based on the Trefftz method

Author

Listed:
  • Yan Su

    (Fuzhou University)

  • Bin Huang

    (Fuzhou University)

  • Lingjun Yang

    (Fuzhou University)

  • Xiaohe Lai

    (Fuzhou University)

  • Chuan Lin

    (Fuzhou University)

  • Xiudong Xie

    (Fuzhou University)

  • Lidan Hong

    (Fujian University of Technology)

Abstract

Detecting water head is crucial in groundwater utilization, and requires quick and accurate solutions. This study employs a method combining the collocation Trefftz method (CTM) and the fictitious time integration method (FTIM) for groundwater head detection and restoration. The Laplace equation is solved using CTM, and the Trefftz basis function is linearly combined to fit the exact solution while adding characteristics length for numerical stability. The FTIM solves the nonlinear algebraic equations system for water head detection. Numerical examples quantify the method's accuracy, and boundary restoration results are compared with the Picard successive approximation method, showcasing FTIM's advantages in convergence steps and precision. The solution comparison under irregular boundary conditions further verifies the proposed method's efficacy (MAE ≤ 10–15). The CTM–FTIM calculated water level boundary aligns with the actual boundary, and its noise immunity is verified using real observation well data (MAE ≤ 10–2, Itertimes ≤ 5000). The CTM–FTIM method eliminates meshing needs for quick solutions in irregular regions, accurately determining water levels in the study domain using few known boundary points, solving infinite domain groundwater head detection.

Suggested Citation

  • Yan Su & Bin Huang & Lingjun Yang & Xiaohe Lai & Chuan Lin & Xiudong Xie & Lidan Hong, 2024. "Study on the detection of groundwater boundary based on the Trefftz method," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 120(8), pages 8057-8085, June.
    • Handle: RePEc:spr:nathaz:v:120:y:2024:i:8:d:10.1007_s11069-024-06534-z
    DOI: 10.1007/s11069-024-06534-z
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    References listed on IDEAS

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    1. Li-Dan Hong & Cheng-Yu Ku & Chih-Yu Liu, 2022. "A Novel Space-Time Marching Method for Solving Linear and Nonlinear Transient Problems," Mathematics, MDPI, vol. 10(24), pages 1-16, December.
    2. Ji Huang & Hongguan Lyu & Chia-Ming Fan & Jiahn-Hong Chen & Chi-Nan Chu & Jiayang Gu, 2020. "Wave-Structure Interaction for a Stationary Surface-Piercing Body Based on a Novel Meshless Scheme with the Generalized Finite Difference Method," Mathematics, MDPI, vol. 8(7), pages 1-22, July.
    3. Ye, Zuyang & Fan, Qingli & Huang, Shibing & Cheng, Aiping, 2021. "A one-dimensional line element model for transient free surface flow in porous media," Applied Mathematics and Computation, Elsevier, vol. 392(C).
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