Symmetry reductions and group-invariant solutions for models arising in water and contaminant transport
Date
2018
Authors
Ntsime, B.P
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Abstract
In this work we consider convection-diffusion equation (CDE) arising in the theory
of contamination of water by oil spill. Furthermore, these equations arise in so
lute transport and groundwater. Group classification of the one dimensional CDE
which depends on time t and space x is performed. Lie point symmetries of the
one-dimensional CDE are obtained. Group invariant solutions are constructed using
admitted Lie point symmetries and these solutions are used to reduce the CDE to
the ordinary differential equations (ODEs), which in most cases are solvable. In cases
where a number of symmetries are obtained, we will construct the one-dimensional
optimal systems of sub-algebras.
The two-dimensional and three dimensional CDE in solute transport with constant
dispersion coefficient is considered. In some of these cases, double reduction meth
ods will be used. Exact solutions are obtained using the Lie symmetry method in conjunction with the (G0/G)-expansion method and the substitution w(z) = (z0)−1 .
To further our studies, we apply the method of potential symmetries to determine
group invariant solutions that cannot be obtained using point symmetries.
Finally, the non-classical symmetries are obtained and comparison study is done
between the results obtained through nonlocal and nonclassical symmetry methods.
Description
A thesis submitted to the Faculty of Science in fulfilment of the requirement for the degree Doctor of Philosophy (PhD), University of the Witwatersrand, School of Computer Science and Applied Mathematics, Johannesburg, 2018
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Citation
Ntsime, Basetsana Pauline (2018) Symmetry reductions and group-invariant solutions for models arising in water and contaminant transport, University of the Witwatersrand, Johannesburg, https://hdl.handle.net/10539/26298