Fuzzy Solution to the Unconfined Aquifer Problem

Abstract

In this article, the solution to the fuzzy second order unsteady partial differential equation (Boussinesq equation) is examined, for the case of an aquifer recharging from a lake. In the examined problem, there is a sudden rise and subsequent stabilization of the lake’s water level, thus the aquifer is recharging from the lake. The aquifer boundary conditions are fuzzy and create ambiguities to the solution of the problem. Since the aforementioned problem concerns differential equations, the generalized Hukuhara (gH) derivative was used for total derivatives, as well as the extension of this theory concerning partial derivatives. The case studies proved to follow the generalized Hukuhara (gH) derivative conditions and they offer a unique solution. The development of the aquifer water profile was examined, as well as the calculation of the recharging fuzzy water movement profiles, velocity, and volume, and the results were depicted in diagrams. According to presented results, the hydraulic engineer, being specialist in irrigation projects or in water management, could estimate the appropriate water volume quantity with an uncertainty level, given by the α-cuts.