A dissertation submitted to the Faculty of Science,
University of the Witwatersrand, in ful llment of the
requirements for the degree of Master of Science.
March 27, 2013 / The transport of chemicals through soils to the groundwater or precipitation
at the soils surfaces leads to degradation of the resources such as soil fertility,
drinking water and so on. Serious consequences may be su ered in the long
run. In this dissertation, we consider macroscopic deterministic models de-
scribing contaminant transport in saturated soils under uniform radial water
ow backgrounds. The arising convection-dispersion equation given in terms
of the stream functions is analyzed using classical Lie point symmetries. A
number of exotic Lie point symmetries are admitted. Group invariant solu-
tions are classi ed according to the elements of the one-dimensional optimal
systems. We analyze the group invariant solutions which satisfy some physical
boundary conditions.
The governing equation describing movements of contaminants under ra-
dial water
ow background may be given in conserved form. As such, the
conserved form of the governing equation may be written as a system of rst
order partial di erential equation referred to as an auxiliary system, by an in-
troduction of the nonlocal variable. The resulting system of equations admits
a number of (local) point symmetries which induce the nonlocal symmetries
for the original governing equation. We construct classes of solutions using the
admitted genuine nonlocal symmetries, which include the invariant solutions
obtained via corresponding point symmetries of the governing equation.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/13004 |
| Date | 06 August 2013 |
| Creators | Potsane, Moshe Moses |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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