Title

Lie group symmetry analysis of transport in porous media with variable transmissivity

RIS ID

25971

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.

Please refer to publisher version or contact your library.

Share

COinS
 

Link to publisher version (DOI)

http://dx.doi.org/10.1016/j.jmaa.2007.09.042