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Article
Lie group symmetry analysis of transport in porous media with variable transmissivity
Faculty of Informatics - Papers (Archive)
  • James M Hill
  • Maureen P Edwards, University of Wollongong
  • A P S Selvadurai
RIS ID
25971
Publication Date
1-1-2008
Publication Details
Edwards, M. P., Selvadurai, A. & Hill, J. (2008). Lie group symmetry analysis of transport in porous media with variable transmissivity. Journal of Mathematical Analysis and Applications, 341 (2), 906-921.
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.
Citation Information
James M Hill, Maureen P Edwards and A P S Selvadurai. "Lie group symmetry analysis of transport in porous media with variable transmissivity" (2008) p. 906 - 921
Available at: http://works.bepress.com/medwards/2/