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Title: Early-time solution of the horizontal unconfined aquifer in the buildup phase
Authors: Gravanis, Elias 
Akylas, Evangelos 
Keywords: Analytical solution;Asymptotic series;Buildup phase;Power series;Unconfined horizontal aquifer
Category: Mathematics
Field: Natural Sciences
Issue Date: Oct-2017
Publisher: Blackwell Publishing Ltd
Source: Water Resources Research, 2017, Volume 53, Issue 10, Pages 8310-8326
Abstract: We derive the early-time solution of the Boussinesq equation for the horizontal unconfined aquifer in the buildup phase under constant recharge and zero inflow. The solution is expressed as a power series of a suitable similarity variable, which is constructed so that to satisfy the boundary conditions at both ends of the aquifer, that is, it is a polynomial approximation of the exact solution. The series turns out to be asymptotic and it is regularized by resummation techniques that are used to define divergent series. The outflow rate in this regime is linear in time, and the (dimensionless) coefficient is calculated to eight significant figures. The local error of the series is quantified by its deviation from satisfying the self-similar Boussinesq equation at every point. The local error turns out to be everywhere positive, hence, so is the integrated error, which in turn quantifies the degree of convergence of the series to the exact solution.
ISSN: 00431397
Rights: © 2017. American Geophysical Union.
Type: Article
Appears in Collections:Άρθρα/Articles

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