Analytical modeling of 2D groundwater flow in a semi-infinite heterogeneous domain with variable lateral sources

Ping-Cheng Hsieh; Po-Wen Yu; Ming-Chang Wu; Ping-Cheng Hsieh; Po-Wen Yu; Ming-Chang Wu

doi:10.3934/math.2024495

AIMS Mathematics

2024, Volume 9, Issue 4: 10121-10140. doi: 10.3934/math.2024495

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Analytical modeling of 2D groundwater flow in a semi-infinite heterogeneous domain with variable lateral sources

Department of Soil and Water Conservation, National Chung Hsing University, Taichung 40227, Taiwan

Received: 11 December 2023 Revised: 29 February 2024 Accepted: 07 March 2024 Published: 13 March 2024
MSC : 76S05

In nature, aquifers are usually composed of distinct kinds of media, i.e., heterogeneous domains rather than homogeneous domains. Groundwater level and flow changes in such domains are more complicated than those in homogeneous domains; thus, building a mathematical model for addressing groundwater flow in heterogeneous aquifers is the present research goal. In conventional research on similar topics, many one-dimensional (1D) analytical models have been presented, but it is challenging to simulate real-world scenarios. This study develops a two-dimensional (2D) analytical model for modeling groundwater flow in a conceptual sloping heterogeneous domain imposed by variable recharge. This model can consider distinct slope angles, medium heterogeneity, and any type of lateral recharge for a semi-infinite domain. The results indicate that groundwater level and flow discharge are greatly affected by the abovementioned factors. The recharge intensity significantly affects the peak of the groundwater level. For example, when the recharge rate increases by 30%, the peak water level increases by 50% as the groundwater flows from the sandy loam zone to the loam zone. The loops delineating the relationship between discharge and groundwater level for different bottom slopes cannot become close for heterogeneous aquifers. The presented 2D analytical model can simulate and better predict results of groundwater changes than previous 1D analytical models. Further, this model can simultaneously consider the effect of varying recharge over time and space on groundwater level change.
- 2D Boussinesq equation,
- heterogeneity,
- semi-infinite domain,
- groundwater recharge,
- anisotropy
Citation: Ping-Cheng Hsieh, Po-Wen Yu, Ming-Chang Wu. Analytical modeling of 2D groundwater flow in a semi-infinite heterogeneous domain with variable lateral sources[J]. AIMS Mathematics, 2024, 9(4): 10121-10140. doi: 10.3934/math.2024495

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Abstract

In nature, aquifers are usually composed of distinct kinds of media, i.e., heterogeneous domains rather than homogeneous domains. Groundwater level and flow changes in such domains are more complicated than those in homogeneous domains; thus, building a mathematical model for addressing groundwater flow in heterogeneous aquifers is the present research goal. In conventional research on similar topics, many one-dimensional (1D) analytical models have been presented, but it is challenging to simulate real-world scenarios. This study develops a two-dimensional (2D) analytical model for modeling groundwater flow in a conceptual sloping heterogeneous domain imposed by variable recharge. This model can consider distinct slope angles, medium heterogeneity, and any type of lateral recharge for a semi-infinite domain. The results indicate that groundwater level and flow discharge are greatly affected by the abovementioned factors. The recharge intensity significantly affects the peak of the groundwater level. For example, when the recharge rate increases by 30%, the peak water level increases by 50% as the groundwater flows from the sandy loam zone to the loam zone. The loops delineating the relationship between discharge and groundwater level for different bottom slopes cannot become close for heterogeneous aquifers. The presented 2D analytical model can simulate and better predict results of groundwater changes than previous 1D analytical models. Further, this model can simultaneously consider the effect of varying recharge over time and space on groundwater level change.

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