New model to capture the conversion of flow from confined to unconfined
Morakaladi, Makosha Ishmaeline Charlotte
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The conversion of flow from confined to unconfined aquifers, while it has attracted the attention of many researchers within and outside of the field of geo-hydrology, although many results and mathematical models have been suggested to replicate such a physical problem, one will inform that, up to now the phenomena has not yet been fully understood. The available literature provides some important mathematical model that can be used to replicate the conversion; however, it is clear that such a model is highly nonlinear as the numerical simulation suggests high value decrease in water level. Such a mathematical model cannot really be used for practical purpose. In this work, a new mathematical model is suggested to minimize high nonlinearity also the mathematical model includes into the mathematical formulation the fading memory effect due to the properties of geological formations. The new model suggested here is a system that consists of partial differential equations, where the first equation presents the flow within the confined aquifer, Theis suggested such a model. The second model is an integro-differential partial differential equation, with a new fading memory term. Due to the complexity of the second equations, we adopted a numerical scheme known as Adams-Bashforth to derive the numerical solution. Using the Von Neumann stability analysis, conditions under which the used numerical scheme is efficient have been established. Numerical simulations have been performed using a mathematical software called Matlab. The mathematical model suggested in this thesis will open doors for new investigation and could be extended to 3-dimensional case, also the model could be extended to the framework of fractional differentiation and integration.