- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Advances in Mathematical Physics
Volume 2014 (2014), Article ID 138289, 11 pages
Classification of the Group Invariant Solutions for Contaminant Transport in Saturated Soils under Radial Uniform Water Flows
Center for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa
Received 8 November 2013; Revised 9 December 2013; Accepted 10 December 2013; Published 2 February 2014
Academic Editor: Waqar Khan
Copyright © 2014 M. M. Potsane and R. J. Moitsheki. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- F. Catania, M. Massabò, and O. Paladino, “Estimation of transport and kinetic parameters using analytical solutions of the 2D advection-dispersion-reaction model,” Environmetrics, vol. 17, no. 2, pp. 199–216, 2006.
- P. Broadbridge, J. M. Hill, and J. M. Goard, “Symmetry reductions of equations for solute transport in soil,” Nonlinear Dynamics, vol. 22, no. 1, pp. 15–27, 2000.
- P. Broadbridge, R. J. Moitsheki, and M. P. Edwards, “Analytical solutions for two dimensional solute transport with velocity-dependent dispersion,” Environmental Mechanics, vol. 129, pp. 145–153, 2002.
- R. J. Moitsheki, P. Broadbridge, and M. P. Edwards, “Group invariant solutions for two dimensional solute transport under realistic water flows,” Quaestiones Mathematicae, vol. 29, no. 1, pp. 73–83, 2006.
- R. J. Moitsheki, Invariant solutions for transient solute transport in saturated and unsaturated soil [Ph.D. thesis], University of Wollongong, 2004.
- J. R. Philip, “Some exact solutions of convection-diffusion and diffusion equations,” Water Resources Research, vol. 30, no. 12, pp. 3545–3551, 1994.
- J. R. Craig and T. Heidlauf, “Coordinate mapping of analytical contaminant transport solutions to non-uniform flow fields,” Advances in Water Resources, vol. 32, no. 3, pp. 353–360, 2009.
- J. E. Houseworth and J. Leem, “A quasilinear model for solute transport under unsaturated flow,” Vadose Zone Journal, vol. 8, no. 4, pp. 1031–1037, 2009.
- J.-S. Chen, C.-F. Ni, and C.-P. Liang, “Analytical power series solutions to the two-dimensional advection-dispersion equation with distancedependent dispersivities,” Hydrological Processes, vol. 22, pp. 4670–4678, 2008.
- R. R. Yadav, D. K. Jaiswal, H. K. Yadav, and G. Gulrana, “Analytical solutions for temporally dependent dispersion through homogeneous porous media,” International Journal of Hydrology Science and Technology, vol. 1, no. 2, pp. 101–115, 2012.
- E. M. E. Zayed and H. A. Zedan, “Autonomous forms and exact solutions of equations of motion of polytropic gas,” International Journal of Theoretical Physics, vol. 40, no. 6, pp. 1183–1196, 2001.
- C. V. Chrysikopoulos and Y. Sim, “One-dimensional virus transport in homogeneous porous media with time-dependent distribution coefficient,” Journal of Hydrology, vol. 185, no. 1–4, pp. 199–219, 1996.
- Y. Sim and C. V. Chrysikopoulos, “Three-dimensional analytical models for virus transport in saturated porous media,” Transport in Porous Media, vol. 30, no. 1, pp. 87–112, 1998.
- Y. Sim and C. V. Chrysikopoulos, “Analytical solutions for solute transport in saturated porous media with semi-infinite or finite thickness,” Advances in Water Resources, vol. 22, no. 5, pp. 507–519, 1999.
- J. M. Thomas and C. V. Chrysikopoulos, “Experimental investigation of acoustically enhanced colloid transport in water-saturated packed columns,” Journal of Colloid and Interface Science, vol. 308, no. 1, pp. 200–207, 2007.
- J. Woods, C. T. Simmons, and K. A. Narayan, “Verification of black box groundwater models,” in Proceedings of the 3rd Biennial Engineering Mathematics and Applications Conference (EMAC '98), pp. 523–526, Institution of Engineers Australia, Adelaide, Australia, 1985.
- D. Hillel, Environmental Soil Physics, Academic Press, New York, NY, USA, 1998.
- J. Bear and A. Verruijt, Modeling Groundwater Flow and Pollution, Kluwer Academic Publishers, Norwell, Mass, USA, 1987.
- G. Ségol, Classical Groundwater Simulation: Proving and Improving Numerical Models, Prentice-Hall, Englewood Cliffs, NJ, USA, 1994.
- J. M. Díaz, YaLie User’s Manual, Departamento de Matemáticas, Universidad de Cádiz, 2000.
- A. C. Hearn, Reduce User’s Manual Version 3.4, Rand Publication CP78, The Rand Corporation, Santa Monica, Calif, USA, 1985.
- J. Sherring, Dimsym: Symmetry Determination and Linear Differential Equation Package, Latrobe University Mathematics Department, Melbourne, Australia, 1993.
- P. J. Olver, Applications of Lie Groups to Differential Equations, Springer, New York, NY, USA, 1972.
- G. W. Bluman and S. C. Anco, Symmetry and Integration Methods for Differential Equations, vol. 154, Springer, New York, NY, USA, 2002.
- G. W. Bluman, A. F. Cheviakov, and S. C. Anco, Applications of Symmetry Methods to Partial Differential Equations, Springer, New York, NY, USA, 2010.
- N. H. Ibragimov, Elementary Lie Group Analysis and Ordinary Differential Equations, vol. 4, John Wiley & Sons, New York, NY, USA, 1999.
- M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover, New York, NY, USA, 1972.
- G. R. Fulford and P. Broadbridge, Industrial Mathematics: Case Studies in the Diffusion of Heat and Matter, Cambridge University Press, Cambridge, UK, 2002.