Lie group symmetry analysis of transport in porous media with variable transmissivity |
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| Authors: | M.P. Edwards James M. Hill |
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| Affiliation: | a School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, Australia
b Department of Civil Engineering and Applied Mechanics, McGill University, 817 Sherbrooke Street West, Montreal, QC H3A 2K6, Canada |
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| Abstract: | We determine the Lie group symmetries of the coupled partial differential equations governing a novel problem for the transient flow of a fluid containing a solidifiable gel, through a hydraulically isotropic porous medium. Assuming that the permeability (K∗) of the porous medium is a function of the gel concentration (c∗), we determine a number of exact solutions corresponding to the cases where the concentration-dependent permeability is either arbitrary or has a power law variation or is a constant. Each case admits a number of distinct Lie symmetries and the solutions corresponding to the optimal systems are determined. Some typical concentration and pressure profiles are illustrated and a specific moving boundary problem is solved and the concentration and pressure profiles are displayed. |
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| Keywords: | Pollutants Porous media Variable permeability Coupled partial differential equations Lie symmetries Exact solutions |
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