Analysis of exact groundwater model within a confined aquifer
Mathobo, Mashudu Clifford
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The main aim of this research was to develop the exact groundwater flow model within a confined aquifer. We argued that, the Theis groundwater flow model is an approximation of the real formulation of the model as he removed some components of the equation to have a simple model. Initially, we derived an exact groundwater flow equation for a confined aquifer so as to include all high order terms that was removed by Theis and also to take into account the assumptions that was used during the derivation of the groundwater flow by Theis. Thereafter, we proved that the new groundwater flow equation has unique solution. We then derived a new numerical scheme for singular partial differential equation that combines the Mellin transform and the Lagrange approximation of a continuous function. The Mellin transform was used to remove the singularity in the newly developed exact groundwater flow equation for a confined aquifer. The equation became ordinary, wherein we used the Adam Bashforth method to the ordinary differential equation in Mellin space. The inverse of Mellin was then used to get the exact numerical scheme in real space. The derivation of the exact solution of groundwater flow equation for a confined aquifer was derived and shown using the Boltzmann transform. We presented the stability analysis of the new numerical scheme using the von Neumann method. We also discussed the application of data in groundwater modelling. We argued that, most methods used in the collection of data lead to incorrect representation of reality or the system under investigation. The application of mathematics to aid in data processing was also suggested. Various interpolation methods used in groundwater were also discussed. We proposed the concept of Multi-step interpolation technique. Lastly, numerical simulations using experimental field data was presented. Our solution was compared to Theis. Our simulations show the importance of scaling factor which was removed from the Theis groundwater flow equation. The simulations also show that the change in drawdown depend on the scaling factor.