Abstract
Solute transport in saturated soil is represented by anonlinear system consisting of a Fokker–Planck equation coupled toLaplace's equation. Symmetries, reductions and exact solutions are foundfor two dimensional transient solute transport through some nontrivialwedge and spiral steady water flow fields. In particular, the mostgeneral complex velocity potential is determined, such that the soluteequation admits a stretching group of transformations that wouldnormally be possessed by a point source solution.
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References
Jury, W. A., ‘Solute transport and dispersion’, in Flow and Transport in the Natural Environment: Advances and Applications, W. L. Steffen and O. T. Denmead (eds.), Springer-Verlag, Berlin, 1988, pp. 1-16.
Woods, J., Simmons, C. T., and Narayan, K. A., ‘Verification of black box groundwater models’, in EMAC98 Proceedings of the Third Biennial Engineering Mathematics and Applications Conference, E. O. Tuck and J. A. K. Stott (eds.), Institution of Engineers Australia, Adelaide, 1998, pp. 523-526.
Wierenga, P. J., ‘Water and solute transport and storage’, in Handbook of Vadose Zone Characterization and Monitoring, L. G. Wilson, G. E. Lorne, and S. J. Cullen (eds.), Lewis Publishers, Boca Raton, FL, 1995, pp. 41-60.
Ségol, G., Classic Groundwater Simulations: Proving and Improving Numerical Models, Prentice Hall, Englewood Cliffs, NJ, 1994.
Salles, J., Thovert, J.-F., Delannay, R., Presons, L., Auriault, J.-L., and Adler, P. M., ‘Taylor dispersion in porous media: Determination of the dispersion tensor’, Physics of Fluids A 5, 1993, 2348-2376.
Philip, J. R., ‘Some exact solutions of convection-diffusion and diffusion equations’, Water Resources Research 30, 1994, 3545-3551.
van Genuchten, M. T. and Alves, W. J., ‘Analytical solutions of the one-dimensional convective-dispersive solute transport equation’, U.S. Department of Agriculture, Technical Bulletin 1661, 1982, 1-151.
Philip, J. R., ‘Theory of infiltration’, Advances in Hydrosciences 5, 1969, 215-296.
Sherring, J., ‘DIMSYM: Symmetry determination and linear differential equations package’, Research Report, Latrobe University Mathematics Department, 1993, http://www.latrobe.edu.au/www/mathstats/ Maths/Dimsym/
Maas, L. R. M., ‘A closed form Green function describing diffusion in a strained flow field’, SIAM Journal of Applied Mathematics 49, 1989, 1359-1373.
Zoppou, C. and Knight, J. H., ‘Analytical solution of a spatially variable coefficient advection-diffusion equation in one-, two-and three-dimensions’, Preprint, CSIRO, Land and Water, Canberra, 1998.
Abramowitz, M. and Stegun, I. A. (eds.), Handbook of Mathematical Functions, Dover, New York, 1972.
Redfern, D., The Maple Handbook, Springer-Verlag, New York, 1996.
Ibragimov, N. H. (ed.) CRC Handbook of Lie Group Analysis of Differential Equations, Vol. 2, Section 8.12.1, CRC Press, Boca Raton, FL, 1996.
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Broadbridge, P., Hill, J.M. & Goard, J.M. Symmetry Reductions of Equations for Solute Transport in Soil. Nonlinear Dynamics 22, 15–27 (2000). https://doi.org/10.1023/A:1008309107295
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DOI: https://doi.org/10.1023/A:1008309107295