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An Explicit Finite Difference Model for Unconfined Aquifers
Author(s) -
Chu Wensen,
Willis Robert
Publication year - 1984
Publication title -
groundwater
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.84
H-Index - 94
eISSN - 1745-6584
pISSN - 0017-467X
DOI - 10.1111/j.1745-6584.1984.tb01441.x
Subject(s) - linearization , aquifer , partial differential equation , nonlinear system , mathematics , finite difference , finite difference method , stability (learning theory) , computer science , control theory (sociology) , mathematical analysis , geotechnical engineering , engineering , groundwater , physics , control (management) , quantum mechanics , machine learning , artificial intelligence
Most of the current simulation models for unconfined aquifers are based on the assumption that the free surface variation is small so that it can be combined with permeability to reduce the nonlinear Boussinesq equation to a linear partial differential equation (PDE). One of the most obvious reasons for using the linearization assumption is for the ease of numerical solution. This work presents a simpler alternative which permits an easy direct solution of the Boussinesq equation. A forward in time, central in space (FTCS) explicit finite difference method is used in the simulation model. The model was first validated by comparing its results with known analytical solution. It was then applied to an actual situation in which the short‐term responses (from pumping) of an unconfined aquifer were simulated. The study shows that the stability of the model can be easily controlled, and because of the simple algorithm used, the code can be expeditiously developed and economically run on smaller machines. Due to the uncertainties in the calibration results, it is recommended here that more data be collected to improve the calibration before the model is used as a real‐time simulation tool.