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Fuzzy analytical solution for the case of a semi-infinite unconfined aquifer
1 , * 1 , 2 , 1
1  Department of rural and Surveying Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
2  Department of Mathematics Kuwait University, Khaldiya Campus, Safat 13060, Kuwait

Abstract:

In this work the analytical solution to the second order fuzzy unsteady partial differential one-dimensional Boussinesq equation is examined. The physical problem concerns unsteady flow in a semi-infinite unconfined aquifer bordering a lake. There is a sudden rise and subsequent stabilization in the water level of the lake, thus the aquifer is recharging from the lake. The fuzzy solution is presented by a simple algebraic equation for the head profiles. This equation requires the knowledge of the initial and boundary conditions as well as the various soil parameters. The above auxiliary conditions are subject to different kinds of uncertainty due to human and machine imprecision and create ambiguities to the solution of the problem and a fuzzy method is introduced. Since the physical problem refers to a partial differential equation, the generalized Hukuhara derivative was used, as well as the extension of this theory regarding the partial derivatives. The objective of this paper is to compare the fuzzy analytical results, with the Runge-Kutta method, in order to prove the reliability and efficiency of the proposed fuzzy analytical method. This comparison attests to the accuracy of the former. Additionally, this results to a fuzzy number for water level profiles as well as for the water volume variation, whose α-cuts, provide, according to Possibility Theory, the water levels and the water volume confidence intervals with probability P=1-α.

Keywords: fuzzy methodology, unsteady flow, Boussinesq equation