Modelling a conversion of a confined to an unconfined aquifer flow
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Date
2019-01
Authors
Magingi, Awodwa
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Publisher
University of the Free State
Abstract
As the human population increases, there is also an increase in water demand for water supply. Due to this increase in demand, groundwater is likely to be over-abstracted to meet the requirements that cannot be met by surface water resources alone. With minimal knowledge and understanding of the different aquifers, the over-abstraction can easily change the natural state of an aquifer, most likely from a confined aquifer conditions to an unconfined aquifer. It is because of this demand that many confined aquifers have been reported to be pumped intensively thus being converted to unconfined aquifers. While some researchers have devoted their attention to understanding this conversion, even also to predict it, we have to point out that several aspects have not been touched in the last decades. We shall point out that the understanding or the prediction of a given natural problem starts with good construction of a mathematical model, so far the studies done were based on local differential operator. It is important to recall that, classical differential operators have been recognized to only predict physical problems following processes with no memory. However, while dealing with the groundwater flow problem, it is important to include the effect of heterogeneity which of course cannot be captured with classical operators. Very recently, some new concepts of differentiation have been suggested, and are called non-local operators, they are able to capture the flow within heterogeneous media, and even the flow is able to follow the Brownian motion and even the random walk. The newly introduced mathematical operator has the ability to describe statistical setting like the Gaussian distribution. More precisely, the operator can capture normal and sub-diffusion, with the crossover in waiting time distribution that ranges from exponential decay law to power law. The aim of this thesis was to analyze the existing model especially the nonlinear one using some newly introduced numerical schemes that have been recognized to be very efficient and powerful mathematical tools. Secondly, the aim was to extend the existing model using the newly introduced differential operator known as the Atangana-Baleanu derivative to provide a numerical scheme that can be used to solve such a model, present the condition under which the scheme is stable and finally the presentation of numerical simulations for different values of alpha using a software package called MATLAB is highlighted and discussed.
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Dissertation (M.Sc. (Geohydrology))--University of the Free State, 2019