Groundwater flow in a two-region aquifer: A 2D analytical solution with recharge forcing

Ming-Chang Wu; Ping-Cheng Hsieh; Ming-Chang Wu; Ping-Cheng Hsieh

doi:10.3934/math.2026233

AIMS Mathematics

2026, Volume 11, Issue 3: 5669-5691. doi: 10.3934/math.2026233

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Research article

Groundwater flow in a two-region aquifer: A 2D analytical solution with recharge forcing

Ming-Chang Wu ¹,
Ping-Cheng Hsieh ^{2
,
,}

1.
National Yunlin University of Science and Technology-Research Center for Soil & Water Resources and Natural Disaster Prevention, Douliu, Yunlin County, Taiwan
2.
Department of Soil and Water Conservation, National Chung Hsing University, Taichung 40227, Taiwan

Received: 11 October 2025 Revised: 14 January 2026 Accepted: 26 February 2026 Published: 05 March 2026
MSC : 76S05

Aquifer systems are often simplified as homogeneous and infinite, yet natural deposits typically display heterogeneity and occur within finite domains. In this study, we developed a two-dimensional analytical framework for groundwater flow in an unconfined two-region aquifer that represents lateral heterogeneity through piecewise hydraulic properties, subjected to spatially variable recharge, formulated using the generalized integral transform technique (GITT). The model was benchmarked against finite-difference simulations of the nonlinear Boussinesq equation, showing close agreement and validating the linearized approach. Applications to contrasting soil properties and recharge patterns revealed that heterogeneity and recharge variability strongly influence groundwater levels and hydraulic gradients. Uniform recharge leads to higher mounding in low-permeability zones, while spatially increasing recharge amplifies head buildup and steepens gradients. In contrast, decreasing recharge shifts the mound toward the aquifer center and produces outward flow. Comparisons between homogeneous and two-region composite aquifers showed that only the latter exhibit abrupt head changes at interfaces. The framework provides a practical tool for groundwater analysis and management.
- groundwater flow,
- heterogeneity,
- recharge,
- 2D analytical model,
- Boussinesq equation
Citation: Ming-Chang Wu, Ping-Cheng Hsieh. Groundwater flow in a two-region aquifer: A 2D analytical solution with recharge forcing[J]. AIMS Mathematics, 2026, 11(3): 5669-5691. doi: 10.3934/math.2026233

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Abstract

Aquifer systems are often simplified as homogeneous and infinite, yet natural deposits typically display heterogeneity and occur within finite domains. In this study, we developed a two-dimensional analytical framework for groundwater flow in an unconfined two-region aquifer that represents lateral heterogeneity through piecewise hydraulic properties, subjected to spatially variable recharge, formulated using the generalized integral transform technique (GITT). The model was benchmarked against finite-difference simulations of the nonlinear Boussinesq equation, showing close agreement and validating the linearized approach. Applications to contrasting soil properties and recharge patterns revealed that heterogeneity and recharge variability strongly influence groundwater levels and hydraulic gradients. Uniform recharge leads to higher mounding in low-permeability zones, while spatially increasing recharge amplifies head buildup and steepens gradients. In contrast, decreasing recharge shifts the mound toward the aquifer center and produces outward flow. Comparisons between homogeneous and two-region composite aquifers showed that only the latter exhibit abrupt head changes at interfaces. The framework provides a practical tool for groundwater analysis and management.

References

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