Homotopy Perturbation Method-Based Analytical Solution for Tide-Induced Groundwater Fluctuations.

Area of Science:

• Hydrogeology
• Fluid Dynamics
• Applied Mathematics

Background:

• Groundwater variations in unconfined aquifers follow the nonlinear Boussinesq's equation.
• Analytical solutions for coastal aquifers under tidal forcing typically use perturbation methods.
• Traditional methods require predefined perturbation parameters, limiting their applicability.

Purpose of the Study:

• To develop a novel, higher-order analytical solution for groundwater fluctuations.
• To address limitations of traditional perturbation methods in coastal aquifer analysis.
• To provide a solution valid for higher amplitude-to-thickness ratios.

Main Methods:

• Utilized the homotopy perturbation method with a virtual perturbation parameter.
• Employed the parameter-expansion method to eliminate secular terms.
• Developed a new dimensional analytical solution.

Main Results:

• The proposed solution does not require predefined perturbation parameters.
• The method is valid for higher values of the amplitude parameter (A/D).
• Successfully removed secular terms, ensuring solution stability.

Conclusions:

• The homotopy perturbation method offers a superior approach for analyzing groundwater fluctuations in coastal aquifers.
• This new analytical solution enhances predictive capabilities for tidal forcing impacts.
• The method provides a more robust and versatile tool for hydrogeological studies.