Analysis of general groundwater flow equation with non-local operators

Simple item page
dc.contributor.advisorAtangana, Abdon
dc.contributor.authorMathobo, Mashudu C.
dc.date.accessioned2021-02-02T07:16:24Z
dc.date.available2021-02-02T07:16:24Z
dc.date.issued2020-01
dc.description.abstractThe main aim of this research was to analyze the general groundwater flow equation with nonlocal operators. Non-local operators are able to introduce the mathematical formulation of memory and random walk. Recently, Mashudu and Mathobo (2017) introduced a more general groundwater flow model which considers the forgotten terms by Theis; however, their model uses the concept of classical differential operators and therefore could not help capture complexities of the media through which the sub-surface water flows. It is in this regard that their model was extended to the concept of non-local operators. The general groundwater flow equation for a confined aquifer was analyzed using the Caputo fractional derivative, Caputo-Fabrizio fractional derivative, AtanganaBaleanu fractional derivative and fractal-fractional differential operators. New numerical schemes were developed using the classical Adam Bash fort method and the newly developed Newton Polynomial method which was developed by Atangana and Araz in 2019. Stability analysis of the numerical schemes were presented. Numerical simulations were developed and showed evidence of three different types of flow according to fractional orders. Slow flow was observed in fractional order from 0.99 to 0.51, depicting that the geological media is not well connected and thus not helping water to pass easily. When the fractional order is below 0.5, fast flow was observed and when the fractional order is 1, normal flow was recovered and the geology was assumed to be homogenous.en_ZA
dc.description.sponsorshipEnvironmental Resource Management (ERM)en_ZA
dc.description.sponsorshipUniversity of Free State Postgraduate Schoolen_ZA
dc.description.sponsorshipWSP Africaen_ZA
dc.description.sponsorshipNational Research Foundation (NRF)en_ZA
dc.identifier.urihttp://hdl.handle.net/11660/10924
dc.language.isoenen_ZA
dc.publisherUniversity of the Free Stateen_ZA
dc.rights.holderUniversity of the Free Stateen_ZA
dc.subjectThesis (Ph.D. (Geohydrology))--University of the Free State, 2020en_ZA
dc.subjectCaputoen_ZA
dc.subjectCaputo-Fabrizioen_ZA
dc.subjectAtangana-Baleanuen_ZA
dc.subjectFractal-Fractional differential operatorsen_ZA
dc.subjectGroundwateren_ZA
dc.subjectConfined aquiferen_ZA
dc.subjectMemoryen_ZA
dc.subjectNumerical Schemeen_ZA
dc.subjectNewton Polynomialen_ZA
dc.subjectFractional calculusen_ZA
dc.subjectGroundwater flow -- Mathematical modelsen_ZA
dc.titleAnalysis of general groundwater flow equation with non-local operatorsen_ZA
dc.typeThesisen_ZA
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
MathoboMC.pdf
Size:
2.4 MB
Format:
Adobe Portable Document Format
Description:
Download
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
1.76 KB
Format:
Item-specific license agreed upon to submission
Description:
Download
Collections
All Electronic Theses and Dissertations