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Early‐Time Solution of the Horizontal Unconfined Aquifer in the Buildup Phase
Author(s) -
Gravanis Elias,
Akylas Evangelos
Publication year - 2017
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1002/2016wr019567
Subject(s) - mathematics , aquifer , dimensionless quantity , series (stratigraphy) , power series , inflow , mathematical analysis , richards equation , exact solutions in general relativity , constant (computer programming) , geotechnical engineering , geology , mechanics , physics , paleontology , groundwater , water content , programming language , computer science
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.