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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:341

Article

Edwards, M. P.¹  Hill, James M.¹  Selvadurai, A. P. S.² 

[1] Univ Wollongong, Sch Math & Appl Stat, Wollongong, NSW 2500, Australia

[2] McGill Univ, Dept Civil Engn & Appl Mech, Montreal, PQ H3A 2K6, Canada

关键词: pollutants;    porous media;    variable permeability;    coupled partial differential equations;    lie symmetries;    exact solutions;   

DOI  :  10.1016/j.jmaa.2007.09.042

来源: Elsevier

【 摘 要 】

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. (C) 2007 Published by Elsevier Inc.

【 授权许可】

Free