On Use of Expanding Parameters and Auxiliary Term in Homotopy Perturbation Method for Boussinesq Equation with Tidal Condition

This paper uses the homotopy perturbation method for the analytical solution of groundwater table fluctuations, in response to the tidal boundary condition, for a coastal unconfined aquifer with sloping beach face. The Boussinesq equation for sloping beach contains two non-linear terms. The governin...

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Bibliographic Details
Published in:Environmental modeling & assessment 2019-02, Vol.24 (1), p.109-120
Main Authors: Munusamy, Selva Balaji, Dhar, Anirban
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Aquifers
Beaches
Boundary conditions
Boussinesq equations
Coastal aquifers
Coordinate transformations
Earth and Environmental Science
Environment
Groundwater
Groundwater levels
Linearity
Math. Appl. in Environmental Science
Mathematical Modeling and Industrial Mathematics
Methods
Nonlinearity
Operations Research/Decision Theory
Parameters
Perturbation methods
Unconfined aquifers
Variation
Water table
Water, Underground
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Summary:This paper uses the homotopy perturbation method for the analytical solution of groundwater table fluctuations, in response to the tidal boundary condition, for a coastal unconfined aquifer with sloping beach face. The Boussinesq equation for sloping beach contains two non-linear terms. The governing equation is reconstructed in homotopic form with two virtual perturbation parameters and an auxiliary term. The secular terms generated from the non-linear diffusion term and the slope term are eliminated by using parameter expansions based on two virtual parameters. Two non-dimensional parameters emerge from the solution in the process of eliminating secular terms: (i) parameter equivalent to amplitude parameter and (ii) parameter representing beach slope. The second-order (starting from zeroth-order) solution is presented. The higher-order solution efficiently captures the non-linearity of the problem.
ISSN:1420-2026
1573-2967
DOI:10.1007/s10666-018-9636-0