Disclosure of the intricacies in coupled groundwater flow and contaminant transport using mesh-less local Petrov–Galerkin method

The study presents the development of the Meshless Local Petrov–Galerkin (MLPG) method to model and predict contaminant transport in porous media which is known as an important issue to prevent the pollution propagation in groundwater. The research focuses on the Rafsanjan Plain in southeastern Iran as a real case study, where no studies of meshless methods have been done. Computational models were implemented using MATLAB, integrating Radial Basis Functions (RBF) as the interpolation technique. The process commenced by establishing a groundwater flow model, where hydraulic head served as the foundational parameter for determining seepage velocity under unsteady-state conditions. Subsequently, the contamination transport was simulated within the aquifer for a period of six months. Comparative analysis between observed empirical data and the modeled values in both flow dynamics and contaminant transport revealed a significant and reasonable alignment. Analysis of the parameters showed that the value of the shape parameter (\({\alpha }_{{\text{c}}})\) can have the greatest impact on achieving a more accurate value. In this research, with \({\alpha }_{{\text{c}}}\)=6 in the contamination transport model, the most reliable outputs were obtained compared to the observed values. Furthermore, the assessment of the coefficient of determination (R² = 0.97) was conducted to evaluate the acceptability of the calibrated parameters. The high R² value suggests a robust correlation between the observed and simulated data, indicating that the model's parameters are within an acceptable range. This finding underscores the accuracy and reliability of the developed MLPG method for analyzing contaminant transport in unconfined aquifers, particularly in the context of the Rafsanjan Plain.