Fuzzy Analytical Solution for the Case of a Semi-Infinite Unconfined Aquifer

Approximate Solutions for Horizontal Unconfined Aquifers in the Buildup Phase

“…while the flow rate is implied by (21). We now define the basic dimensionless variables, namely, the dimensionless coordinate (X), the dimensionless time (T), and the dimensionless height of the water table (H) as follows:…”

“…Therefore, solutions of the Boussinesq equation are important, and the topic of reaching either analytical or approximate solutions remains an active research topic. The current set of known solutions is by no means exhaustive, and many analytical solutions are being continuously proposed by considering different initial and boundary conditions representative for the problem under investigation [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22].…”

“…Another more attractive method is the use of power series solutions for the self-similar form of the Boussinesq equation for the problem of horizontal aquifers, considering a power law boundary condition for the water depth at inlets. The latter form of the solution was obtained in [8,10,11,15,18,21,[27][28][29][30][31][32]. These solutions are useful for the computation of flow volumes either injected into or pumped out from aquifers.…”

“…The approximate solutions are obtained using different mathematical techniques in which, usually, the final expressions are in the form of series expansions of functions constructed for each case that is examined. These include polynomial series expansions, implicit forms, explicit closed-forms, and, lately, fuzzy solutions requiring iterative procedures to converge [7,16,17,21,[30][31][32][40][41][42][43]. The approximate solutions, if they can be developed, present the advantages that, in most cases, are simple and that the mathematical manipulations can be fairly accommodated because they are straightforward and can be easily implemented.…”