Management of Saltwater Intrusion in Sloping Coastal Aquifers Using the Meshless Local Petrov–Galerkin (MLPG) Numerical Method

Document Type : Research Paper

Authors

• Zahra Baazm ¹
• Abolfazl Akbarpour ²
• Mostafa Yaghoubzadeh ³
• Seyed Saeed Eslamian ⁴
• Hossein Khozeymehnezhad ⁵

¹ 1. . PhD Student, Water Science and Engineering, Faculty of Agriculture, University of Birjand, Birjand, Iran.

² Professor, Department of Civil Engineering, Faculty of Engineering, University of Birjand, Birjand, Iran

³ 3. Associate Professor, Department of Water Science and Engineering, Faculty of Agriculture, University of Birjand, Birjand, Iran

⁴ Seyed Saeid Eslamian, Department of Water Science and Engineering, College of Agriculture, Isfahan Univetsity of Technology, Isfahan, Iran

⁵ 5. Associate Professor, Department of Water Science and Engineering, Faculty of Agriculture, University of Birjand, Birjand, Iran

Abstract

Keywords

• Coastal aquifer
• Cutoff wall
• Mesh-free local Petrov-Galerkin method
• Sloping
• Saltwater intrusion

Main Subjects

• منابع آب

Introduction

Coastal aquifers are vital sources of freshwater for densely populated coastal regions. Under natural conditions, groundwater flows from inland areas toward the sea. However, excessive groundwater extraction can reverse the hydraulic gradient, allowing seawater to intrude into aquifers and degrade water quality. Climate change, sea-level rise, and reduced aquifer recharge further intensify this process, increasing the risk of groundwater salinization. Given that nearly 70% of the world’s population lives in coastal zones, managing seawater intrusion has become a major environmental and economic challenge. Among various management solutions, subsurface cutoff walls have been recognized as one of the most effective techniques to control the advancement of the saline front. The present study investigates the influence of aquifer bed slope geometry and cutoff wall depth on the extent of saltwater intrusion using the Meshless Local Petrov–Galerkin (MLPG) numerical method.

Method

In this research, the MLPG numerical model was developed to simulate seawater intrusion in a coastal aquifer. This mesh-free approach eliminates the need for complex grid generation and provides higher accuracy in solving partial differential equations compared to finite element and finite difference methods. Modeling was performed in MATLAB using a computational grid of 231 nodes with a uniform spacing of 0.1 m in both directions. Three aquifer slope geometries were considered: seaward slope (SS), horizontal bed (H), and landward slope (LS). Each geometry was simulated under four cutoff wall depths (0.15, 0.30, 0.45, and 0.60 m) and one scenario without a wall. Model parameters were based on the Henry problem, and the model’s accuracy was validated against the study by Abd-Elaty & Polemio (2023). The statistical indicators RMSE, R², and NSE were used to evaluate the model’s precision and performance.

Results

The findings revealed that increasing the cutoff wall depth significantly reduces seawater intrusion. In the horizontal (H) model, increasing wall depth from 0.15 m to 0.60 m reduced intrusion from 0.93 m to 0.50 m—a 50% reduction. In the landward slope (LS) model, the intrusion decreased from 1.05 m to 0.50 m (52.4%), and in the seaward slope (SS) model, it decreased from 0.90 m to 0.50 m (45%).The LS condition showed the highest saltwater advancement, while the SS condition showed the least. In all models, the 0.60 m cutoff wall depth consistently produced the minimum intrusion (0.50 m) and can therefore be identified as the optimal depth. Statistical validation confirmed the high accuracy of the MLPG model: RMSE < 0.06, R² > 0.95, and NSE > 0.9 in all scenarios, indicating excellent agreement with benchmark data. Sensitivity analysis showed that a ±20% change in hydraulic conductivity (K) caused a 6–9% variation in the position of the saline front, highlighting the importance of accurately defining hydraulic properties in simulation models.

Conclusions

This study demonstrates that aquifer bed geometry and cutoff wall depth have a significant impact on seawater intrusion in coastal aquifers. A landward slope increases intrusion by about 10%, while a seaward slope reduces it by about 5%, compared to the horizontal case. The 0.60 m cutoff wall depth was found to be the most effective and optimal configuration across all scenarios. The high accuracy and numerical stability of the MLPG method confirm its potential as a reliable and efficient tool for modeling and managing coastal groundwater systems.

Author Contributions

Conceptualization A. Akbarpour and Z. Baazm; methodology, , A. Akbarpour; software, Z. Baazm and A. Akbarpour; validation S. S. Islamian and H. Khozaimenejad; formal analysis, A. Akbarpour and Z. Baazm; investigation, M. Yaqubzadeh and H. Khozaimenejad. ; resources, Z. Baazm; data curation Z. Baazm, A. Akbarpour and M. Yaqubzadeh,; writing-original draft preparation, Z. Baazm; writing-review and editing, Z. Baazm, A. Akbarpour, M. Yaqubzadeh and H. Khozaimenejad.; visualization, Z. Baazm and M. Yaqubzadeh; supervision, Z. Baazm and A. Akbarpour,; project management A. Akbarpour and M. Yaqubzadeh; funding acquisition, Z. Baazm and A. Akbarpour. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Data available on request from the authors.

Ethical considerations

The authors avoided data fabrication, falsification, plagiarism, and misconduct.

Conflict of interest

The author declares no conflict of interest.