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ARS Home » Southeast Area » Oxford, Mississippi » National Sedimentation Laboratory » Watershed Physical Processes Research » Research » Publications at this Location » Publication #414150
Research Project: Computational Tools and Decision Support System Technologies for Agricultural Watershed Physical Processes, Water Quality and Ground Water Management

Location: Watershed Physical Processes Research

Title: A stable localized weak strong form radial basis function method for modelling variably saturated groundwater flow induced by pumping and injection

Author
item FANG, JIAYU - University Of Mississippi
item AL-HAMDAN, MOHAMMAD - University Of Mississippi
item O'Reilly, Andrew - Andy
item OZEREN, YAVUZ - University Of Mississippi

Submitted to: Engineering Analysis with Boundary Elements
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 8/11/2024
Publication Date: 8/19/2024
Citation: Fang, J., Al-Hamdan, M.Z., O'Reilly, A.M., Ozeren, Y., 2024. A stable localized weak strong form radial basis function method for modelling variably saturated groundwater flow induced by pumping and injection. Engineering Analysis with Boundary Elements 168: 105922. https://doi.org/10.1016/j.enganabound.2024.105922
DOI: https://doi.org/10.1016/j.enganabound.2024.105922

Interpretive Summary: The unsaturated zone is the shallowest part of an aquifer near the ground surface where the aquifer is not fully saturated with water. Movement of water in the unsaturated zone strongly affects the flow of groundwater that may be caused by a well that pumps water out of or into the aquifer. Traditionally, numerical groundwater models under these conditions focus on only pumping in the fully saturated zone, merely simulate variably saturated groundwater flow without pumping in the aquifer, or require a complex computational mesh, which is an array of points representing geographic locations at regular intervals where the model is applied. To fill this gap, a three-dimensional meshless model, CCHE3D-GW-RBF, was developed for variably saturated groundwater flow with the consideration of pumping and injection. The localized radial basis function (RBF) method was employed in this model. This new model complements our previous meshless model (CCHE3D-GW-Meshless) that was based on the moving least squares (MLS) method. Compared to MLS, RBF is more flexible and easier for programming and possesses the nodal interpolation property that allows more accurate representation of real-world conditions. After verification and validation, CCHE3D-GW-RBF was successfully applied to the Mississippi River Valley alluvial aquifer at an experimental groundwater pumping and injection operation at Shellmound, Mississippi, USA, on April 14-19, 2021. CCHE3D-GW-RBF provides a new decision-support tool that allows scientists to more efficiently model groundwater resources management problems.

Technical Abstract: The unsaturated zone profoundly affects groundwater (GW) flow induced by pumping and injection due to the capillary forces. However, current meshless numerical models for GW pumping and injection mostly ignore the unsaturated zone and only focus on the fully saturated flow. To bridge this gap, a three-dimensional meshless model (CCHE3D-GW-RBF) was developed in this study for variably saturated GW flow with the consideration of pumping and injection. Flow processes in saturated and unsaturated zones were both modelled by the mixed-form Richards equation which was linearized by the modified Picard iteration. The van Genuchten (1980) formulas were employed for the soil-water characteristic curves. Differential operators were approximated by the localized Gaussian radial basis function (RBF). To alleviate the problem of the ill-conditioned interpolation matrix resulting from small RBF shape parameter, the weighted singular value decomposition method was used to construct stable bases. The weak-strong form method was adopted in which the weak formulation using Meshless Local Petrov Galerkin method was imposed on the flux boundaries or at the pumping/injection wells, while the strong-form equation using the collocation RBF method was enforced on the other points. Good agreement was found between the simulation results from CCHE3D-GW-RBF and the analytical/numerical solutions in all three verification cases. A smaller RBF shape parameter was found to produce a more accurate result. The new model was then applied to a field case of extracting GW through a pumping well near a meandering river located at Shellmound, Mississippi, USA, which demonstrates the applicability of the model to real-world problems.