Document Type : Original Article
Authors
1
Assistant Professor, Department of Water Engineering, Lorestan University, Khorramabad, Iran Email: nazeri.mh@lu.ac.ir
2
Associate Professor, Department of Water Engineering, Lorestan University, Khorramabad, Iran, Email: nasrolahi.a@lu.ac.ir
3
Assistant Professor, Department of Water Engineering, University of Torbat Heydarieh, Torbat Heydarieh, Iran
10.22034/hyd.2026.70926.1829
Abstract
This research evaluated and compared the performance of three numerical methods (Finite Difference, Meshless, and Meshfree) for simulating the groundwater level in the Dorud-Borujerd plain aquifer. First, various grid structures, including regular grids with different resolutions (coarse, medium, and fine) and the meshless method, were analyzed. The results showed that while increasing the fineness of the grid in the FDM improves the accuracy of boundary representation, it exponentially increases computational volume and cost and can lead to numerical instability. Subsequently, the simulation performance of each model was evaluated using descriptive statistics, error metrics (such as RMSE, NSE, KGE, R², and PBIAS), and graphical analyses (residuals, box plots, and violin plots). Based on these evaluations, the Meshless model was identified as the most accurate and stable model. This model achieved the lowest root mean square error (RMSE ≈ 2.46 m) and the highest values of the Nash-Sutcliffe efficiency index (NSE=0.99) and the coefficient of determination (R²≈0.999). Additionally, the residual plot revealed that this model has the smallest error dispersion and the closest probability density distribution to the actual data. In contrast, although the FDM model was successful in estimating the mean, it had a higher RMSE error (approximately 11.2 meters) and a lower KGE index (0.76), indicating an imbalance among the various error components. The Meshfree model, despite having an acceptable KGE index, exhibited the greatest systematic deviation (bias) and dispersion in the results. The Meshless method can be the superior choice for stable simulation of groundwater levels in complex environments.
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