Analytical Solution to the One-Dimensional Advection-Diffusion Equation with Temporally Dependent Coefficients

References

[1] A. Ogata and R. B. Banks, “A Solution of the Differential Equation of Longitudinal Dispersion in Porous Media,” US Geological Survey Professional Papers, No. 34, 1961, p. 411-A.

[2] D. R. F. Harleman and R. R. Rumer, “Longitudinal and Lateral Dispersion in an Isotropic Porous Medium,” Journal of Fluid Mechanics, Vol. 16, No. 3, 1963, pp. 385- 394. doi:10.1017/S0022112063000847

[3] V. Guvanasen and R. E. Volker, “Experimental Investigations of Unconfined Aquifer Pollution from Recharge Basins,” Water Resources Research, Vol. 19, No. 3, 1983, pp. 707-717. doi:10.1029/WR019i003p00707

[4] T. J. Marshal, J. W. Holmes and C. W. Rose, “Soil Physics,” 3rd Edition, Cambridge University Press, Cambridge, 1996.

[5] R. B. Banks and J. Ali, “Dispersion and Adsorption in Porous Media Flow,” Journal of Hydraulic Division, Vol. 90, No. 5, 1964, pp. 13-31.

[6] A. Ogata, “Theory of Dispersion in Granular Media,” US Geological Survey Professional Papers, No. 411-1, p. 34, 1970.

[7] S. H. Lai and J. J. Jurinak, “Numerical Approximation of Cation Exchange in Miscible Displacement Through Soil Columns,” Soil Science Society American Proceeding, Vol. 35, No. 6, 1971, pp. 894-899.
doi:10.2136/sssaj1971.03615995003500060017x

[8] M. A. Marino, “Distribution of Contaminants in Porous Media Flow,” Water Resources Research, Vol. 10, No. 5, 1974, pp. 1013-1018. doi:10.1029/WR010i005p01013

[9] A. N. S. Al-Niami and K. R. Rushton, “Analysis of Flow against Dispersion in Porous Media,” Journal of Hydrology, Vol. 33, No. 1-2, 1977, pp. 87-97.
doi:10.1016/0022-1694(77)90100-7

[10] M. Th. van Genuchten and W. J. Alves, “Analytical Solutions of the One Dimensional Convective-Dispersive Solute Transport Equation,” US Department of Agriculture, Technical Bulletin, No. 1661, 1982.

[11] F. T. Lindstrom and L. Boersma, “Analytical Solutions for Convective Dispersive Transport in Confined Aquifers with Different Initial and Boundary Conditions,” Water Resources Research, Vol. 25, No. 2, 1989, pp. 241-256. doi:10.1029/WR025i002p00241

[12] D. K. Jaiswal, A. Kumar, N. Kumar and R. R. Yadav, “Analytical Solutions for Temporally and Spatially DePendent Solute Dispersion of Pulse Type Input ConcenTration in One-Dimensional Semi-Infinite Media,” Journal of Hydro-Environment Research, Vol. 2, 2009, pp. 254-263. doi:10.1016/j.jher.2009.01.003

[13] A. Kumar, D. K. Jaiswal and N. Kumar, “Analytical Solutions to One-Dimensional Advection-Diffusion Equation with Variable Coefficients in Semi-Infinite Media,” Journal of Hydrology, Vol. 380, No. 3-4, 2010, pp. 330-337. doi:10.1016/j.jhydrol.2009.11.008

[14] S. R. Yates, “An Analytical Solution for One Dimensional Transport in Porous Media with an Experimental Dispersion Function,” Water Resources Research, Vol. 28, No. 8, 1992, pp. 2149-2154. doi:10.1029/92WR01006

[15] J. D. Logan and V. Zlotnik, “The convection-Diffusion Equation with Periodic Boundary Conditions,” Applied Mathematics Letter, Vol. 8, No. 3, 1995, pp. 55-61.
doi:10.1016/0893-9659(95)00030-T

[16] J. D. Logan, “Solute Transport in Porous Media with Scale-Dependent Dispersion and Periodic Boundary Conditions,” Journal of Hydrology, Vol. 184, No. 3, 1996, pp. 261-276. doi:10.1016/0022-1694(95)02976-1

[17] M. M. Aral and B. Liao, “Analytical Solutions for Two- Dimensional Transport Equation with Time-Dependent Dispersion Coefficients,” Journal of Hydrologic Engineering, Vol. 1, No. 1, 1996, pp. 20-32.
doi:10.1061/(ASCE)1084-0699(1996)1:1(20)

[18] R. Haberman, “Elementary Applied Partial Differential Equations,” Prentice-Hall, Englewood Cliffs, 1987.

[19] G. Matheron and G. De Marsily, “Is Transport in Porous Media Always Diffusive, a Counterexample,” Water Resources Research, Vol. 16, No. 5, 1980, pp. 901-917.
doi:10.1029/WR016i005p00901

[20] G. Sposito, W. A. Jury and V. K. Gupta, “Fundamental Problems in the Stochastic Convection-Dispersion Model for Solute Transport in Aquifers and Field Soils,” Water Resources Research, Vol. 22, No. 1, 1986, pp. 77-88.
doi:10.1029/WR022i001p00077

[21] L. W. Gelhar, C. Welty and K. R. Rehfeldt, “A Critical Review of Data on Field-Scale Dispersion in Aquifers,” Water Resources Research, Vol. 28, No. 7, 1992, pp. 1955-1974. doi:10.1029/92WR00607

[22] A. Kumar, D. K. Jaiswal and N. Kumar, “Analytical Solutions of One-Dimensional Advection-Diffusion Equation with Variable Coefficients in a Finite Domain,” Journal of Earth System Science, Vol. 118, No. 5, 2009, pp. 539-549. doi:10.1007/s12040-009-0049-y

[23] H. B. Fischer, E. J. List, R. C. Y. Koh, J. Imberger and N. H. Brooks, “Mixing in Inland and Coastal Waters,” Academic Press, New York, 1979.