Department of Civil Engineering
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Item Analytical solution of groundwater waves in unconfined aquifers with sloping boundary(Springer, 2017-07) Munusamy, Selva BalajiA new analytical solution is derived for tide-driven groundwater waves in coastal aquifers using higher-order Boussinesq equation. The homotopy perturbation solution is derived using a virtual perturbation approach without any pre-defined physical parameters. The secular term removal is performed using a combination of parameter expansion and auxiliary term. This approach is unique compared with existing perturbation solutions. The present first-order solution compares well with the previous analytical solutions and a 2D FEFLOW solution for a steep beach slope. This is due to the fact that the higher-order Boussinesq equation captures the streamlines better than ordinary Boussinesq equation based on Dupuit’s assumption. The slope of the beach emerges as an implicit physical parameter from the solution process.Item On Use of Expanding Parameters and Auxiliary Term in Homotopy Perturbation Method for Boussinesq Equation with Tidal Condition(Springer, 2018-10) Munusamy, Selva BalajiThis 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.Item Homotopy Perturbation Method-Based Analytical Solution for Tide-Induced Groundwater Fluctuations(Wiley, 2015-09) Munusamy, Selva BalajiThe groundwater variations in unconfined aquifers are governed by the nonlinear Boussinesq's equation. Analytical solution for groundwater fluctuations in coastal aquifers under tidal forcing can be solved using perturbation methods. However, the perturbation parameters should be properly selected and predefined for traditional perturbation methods. In this study, a new dimensional, higher-order analytical solution for groundwater fluctuations is proposed by using the homotopy perturbation method with a virtual perturbation parameter. Parameter-expansion method is used to remove the secular terms generated during the solution process. The solution does not require any predefined perturbation parameter and valid for higher values of amplitude parameter A/D, where A is the amplitude of the tide and D is the aquifer thickness.