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

Kunwar Gaurav Singh and Tinesh Pathania

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 240, issue C, 332-346

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.

Keywords: Generalized finite difference method (GFDM); Groundwater flow; Meshless; Middle Ganga basin; Moving least squares (MLS) method; Unconfined aquifer (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:240:y:2026:i:c:p:332-346

DOI: 10.1016/j.matcom.2025.07.027

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