Aral, M. M. and Liao, B. (1996). Analytical solutions for two-dimensional transport equation with time-dependent dispersion coefficients. J. Hydrol. Eng., 1(1); 20-32. Basha, H. A. and El-Habel, F. S. (1993). Analytical solution of the one-dimensional time-dependent transport equation. Water Resour. Res., 29(9); 3209-3214. Bear, J. (1972). Dynamics of fluids in porous media. (New York: Elsevier). Belyaev, A. Y., Dzhamalov, R. G., Medovar, Y. A. and Yushmanov, I. O. (2007). Assessment of groundwater inflow in urban territories. Water Resour., 34(5); 496-500. Broadbridge, P., Moitsheki, R. J. and Edwards, M. P. (2002). Analytical solutions for two-dimensional solute transport with velocity-dependent dispersion. Environmental mechanics: water, mass and energy transfer in the biosphere, The Philip Vol., 145-153. Carnahan, C. L. and Remer, J. S. (1984). Nonequilibrium and equilibrium sorption with a linear sorption isotherm during mass transport through an infinite porous medium: some analytical solutions. J. Hydrol., 73(3-4); 227-258. Chatterjee, A. and Singh, M. K. (2018). Two-dimensional advection-dispersion equation with depth-dependent variable source concentration. Pollut., 4(1); 1-8. Chen, J. S., Ni, C. F. and Liang, C. P. (2008). Analytical power series solutions to the two‐dimensional advection-dispersion equation with distance-dependent dispersivities. Hydrol. Processes., 22(24); 4670-4678. Chen, J. S., Chen, J. T., Liu, C. W., Liang, C. P. and Lin, C. W. (2011). Analytical solutions to two-dimensional advection-dispersion equation in cylindrical coordinates in finite domain subject to first-and third-type inlet boundary conditions. J. Hydrol., 405; 522-531. Cremer, C. J., Neuweiler, I., Bechtold, M. and Vanderborght, J. (2016). Solute transport in heterogeneous soil with time-dependent boundary conditions. Vadose Zone J., 15(6); 2-17. Hayek, M. (2016). Analytical model for contaminant migration with time-dependent transport parameters. J. Hydrol. Eng., 21(5); 04016009. Kazezyılmaz-Alhan, C. M. (2008). Analytical solutions for contaminant transport in streams. J. Hydrol., 348(3-4); 524-534. Khebchareon, M. (2012). Crank-Nicolson finite element for 2-D groundwater flow, advection-dispersion and interphase mass transfer: 1. Model development. Int. J. Numer. Anal. Model., Series B, 3(2); 109-125. Kumar, A., Jaiswal, D. K. and Kumar, N. (2009). Analytical solutions of one-dimensional advection-diffusion equation with variable coefficients in a finite domain. J. Earth Syst. Sci., 118(5); 539-549. Logan, J. D. (1996). Solute transport in porous media with scale-dependent dispersion and periodic boundary conditions. J. Hydrol., 184(3-4); 261-276. Maraqa, M. A. (2007). Retardation of nonlinearly sorbed solutes in porous media. J. Environ. Eng., 133(12); 1080-1087. Park, E. and Zhan, H. (2001). Analytical solutions of contaminant transport from finite one-, two-, and three-dimensional sources in a finite-thickness aquifer. J. Contam. Hydrol., 53; 41-61.
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Sanskrityayn, A. and Kumar, N. (2018). Analytical solutions of ADE with temporal coefficients for continuous source in infinite and semi-infinite media. J. Hydrol. Eng., 23(3); 06017008. Sanskrityayn, A., Singh, V. P., Bharati, V. K. and Kumar, N. (2018). Analytical solution of two-dimensional advection-dispersion equation with spatio-temporal coefficients for point sources in an infinite medium using Green’s function method. Environ. Fluid Mech., 18(3); 739-757. Singh, M. K., Begam, S. Thakur, C. K. and Singh, V. P. (2018). Solute transport in a semi-infinite homogeneous aquifer with a fixed-point source concentration. Environ. Fluid Mech., 18(5); 1121-1142. Singh, M. K., Singh, P. and Singh, V. P. (2010). Analytical solution for two-dimensional solute transport in finite aquifer with time-dependent source concentration. J. Eng. Mech., 136(10); 1309-1315. Singh, M. K., Singh, V. P., Singh, P. and Shukla, D. (2009). Analytical solution for conservative solute transport in one-dimensional homogeneous porous formations with time-dependent velocity. J. Eng. Mech., 135(9); 1015-1021. Tadjeran, C. and Meerschaert, M. M. (2007). A second-order accurate numerical method for the two-dimensional fractional diffusion equation. J. Comput. Phys., 220(2); 813-823. Tang, D. H., Frind, E. O. and Sudicky, E. A. (1981). Contaminant transport in fractured porous media: Analytical solution for a single fracture. Water Resour. Res., 17(3); 555-564. Van Duijn, C. J. and van der Zee, S. E. A. T. M. (2018). Large time behaviour of oscillatory nonlinear solute transport in porous media. Chem. Eng. Sci., 183; 86-94. Yates, S. R. (1992). An analytical solution for one-dimensional transport in porous media with an exponential dispersion function. Water Resour. Res., 28(8); 2149-2154. Wang, K. and Huang, G. (2011). Effect of permeability variations on solute transport in highly heterogeneous porous media. Adv. Water Resour., 34(6); 671-683. Zhan, H., Wen, Z., Huang, G. and Sun, D. (2009). Analytical solution of two-dimensional solute transport in an aquifer-aquitard system. J. Contam. Hydrol., 107; 162-174.
Zheng, C. and Bennett, G. D. (2002). Applied Contaminant Transport Modeling. Second ed. (Wiley: New York). Zogheib, B. and Tohidi, E. (2016). A new matrix method for solving two-dimensional time-dependent diffusion equations with Dirichlet boundary conditions. Appl. Math. Comput., 291; 1-13.