Classical lie point symmetry analysis of models arising in contaminant transport theory

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.