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Development and real field application of meshless generalized finite difference method for unconfined groundwater flow modelling

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  • Singh, Kunwar Gaurav
  • Pathania, Tinesh

Abstract

The present study introduces a meshless generalized finite difference method (GFDM) framework to simulate the unconfined groundwater flow in an aquifer. GFDM applies the Taylor series and moving least squares (MLS) method to compute the spatial derivatives and obtain the system of equations. For modelling complex aquifer systems, the meshless methods are more suitable due to the use of scattered nodes. Among these, differential-based strong-form methods are more desirable because of their simplicity and computational efficiency. However, such available models linearize the non-linear unconfined flow equation in the head (h), resulting in computing extra global matrices. The proposed model solves for h2, thereby reducing the global matrices and computational efforts of GFDM to obtain the head solution. In the present work, the GFDM model is first applied to a hypothetical two-dimensional (2-D) problem and validated with a MODFLOW solution. GFDM model is also successfully tested with regular and irregular distribution of nodes. Thereafter, a real field application of the model is presented for an unconfined aquifer of 11470 km2 area in the Middle Ganga Plain in Bihar, India, where three rivers and a hill also make its boundary. The extensive groundwater withdrawal of this aquifer is represented by the 2262 pumping wells assigned at all field nodes. With the proposed approach, the GFDM head solution for this complex aquifer also matched closely with the MODFLOW solution. This study indicates that the developed model is straightforward and possesses robustness in simulating the unconfined flow of real-world problems.

Suggested Citation

  • Singh, Kunwar Gaurav & Pathania, Tinesh, 2026. "Development and real field application of meshless generalized finite difference method for unconfined groundwater flow modelling," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 240(C), pages 332-346.
    • Handle: RePEc:eee:matcom:v:240:y:2026:i:c:p:332-346
    DOI: 10.1016/j.matcom.2025.07.027
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    References listed on IDEAS

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    1. Ambast, S.K. & Tyagi, N.K. & Raul, S.K., 2006. "Management of declining groundwater in the Trans Indo-Gangetic Plain (India): Some options," Agricultural Water Management, Elsevier, vol. 82(3), pages 279-296, April.
    2. Tinesh Pathania & Andrea Bottacin-Busolin & A. K. Rastogi & T. I. Eldho, 2019. "Simulation of Groundwater Flow in an Unconfined Sloping Aquifer Using the Element-Free Galerkin Method," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(8), pages 2827-2845, June.
    3. Pang-Wei Liu & James S. Famiglietti & Adam J. Purdy & Kyra H. Adams & Avery L. McEvoy & John T. Reager & Rajat Bindlish & David N. Wiese & Cédric H. David & Matthew Rodell, 2022. "Groundwater depletion in California’s Central Valley accelerates during megadrought," Nature Communications, Nature, vol. 13(1), pages 1-11, December.
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