Classical lie point symmetry analysis of models arising in contaminant transport theory
Date
2014-03-05
Authors
Mkhonta, Zwelithini Fanelo
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Abstract
Groundwater contamination and soil salinisation are a major environmental
problem worldwide. Living organisms depend largely on groundwater for their
survival and its pollution is of course of major concern. It therefore goes
without saying that remedial processes and understanding of the mathematical
models that describe contaminant transport is of great importance. The theory
of contaminant transport requires understanding of the water
ow even at
the microscopic level. In this study we focus on macroscopic deterministic
models based on di erential equations. Here contaminant will refer to
nonreactive contaminant. We aim to calculate Lie point symmetries of the
one-dimensional Advection-di usion equation (ADE) for various forms of the
di usion coe cient and transport velocity. We aim to employ classical Lie
symmetry techniques. Furthermore, reductions will be carried out using
the elements of the optimal systems. In concluding, the ADE is analyzed
for selected forms of the the di usion coe cient and transport velocity via
the potential symmetry method. For the potential symmetries obtained, we
investigate the associated invariant solutions.