حل تحلیلی معادله دو بعدی و غیرماندگار انتقال آلودگی به‌ازای شرط اولیه و منابع آلاینده دلخواه در مجاری روباز

Aral, M. M. and Liao, B., 1996, Analytical solutions for two-dimensional transport equation with time-dependent dispersion coefficients., Journal of Hydrologic Engineering 1(1), 20-32.

Basha, H., 1997, Analytical model of two-dimensional dispersion in laterally nonuniform axial velocity distributions., Journal of Hydraulic Engineering 123(10), 853-862.

Cassol, M., Wortmann, S. and Rizza, U., 2009, Analytic modeling of two-dimensional transient atmospheric pollutant dispersion by double GITT and Laplace Transform techniques., Environmental Modelling Software 24(1), 144-151.

Chapra, S. C., 1997, Surface water-quality modeling, McGraw-Hill New York.

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., Journal of Hydrology 405(3-4), 522-531.

Chen, K., Zhan, H. and Zhou, R., 2016, Subsurface solute transport with one-, two-, and three-dimensional arbitrary shape sources., Journal of contaminant hydrology 190, 44-57.

Costa, C. P., Vilhena, M. T., Moreira, D. M. and Tirabassi, T., 2006, Semi-analytical solution of the steady three-dimensional advection-diffusion equation in the planetary boundary layer., 40(29), 5659-5669.

Cotta, R. M., 1993, Integral transforms in computational heat and fluid flow, CRC Press.

Cotta, R. M., Knupp, D. C. and Naveira Cotta, C. P., 2016, Analytical heat and fluid flow in microchannels and microsystems, Springer.

Cotta, R. M. and Mikhailov, M. D., 1997, Heat conduction: lumped analysis, integral transforms, symbolic computation, Wiley Chichester.

De Almeida, G. L., Pimentel, L. C. and Cotta, R. M., 2008, Integral transform solutions for atmospheric pollutant dispersion., Environmental Modeling Assessment, 13(1), 53-65.

De Barros, F. P., Mills, W. B. and Cotta, R. M., 2006, Integral transform solution of a two-dimensional model for contaminant dispersion in rivers and channels with spatially variable coefficients., Environmental Modelling Software 21(5), 699-709.

De Barros, F. P. and Cotta, R. M. J., 2007, Integral transforms for three-dimensional steady turbulent dispersion in rivers and channels., Applied Mathematical Modelling 31(12), 2719-2732.

Guerrero, J. P., Pimentel, L. C., Skaggs, TH. and Van Genuchten, M. Th., 2009, Analytical solution of the advection–diffusion transport equation using a change-of-variable and integral transform technique., International Journal of Heat Mass Transfer 52(13-14), 3297-3304.

Mashhadgarme, N., Mazaheri, M. and Mohammad Vali Samani, J., 2017, Analytical solutions to one- and two-dimensional Advection-Dispersion-Reaction equation with arbitrary source term time pattern using Green’s function method., Sharif Journal of Civil Engineering, 33-2, 77-91.

Sanskrityayn, A., Singh, V., 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. Environmental Fluid Mechanics 18(3), 739-757.

Van Genuchten, M. Th., Leij, F. J., Skaggs, T. H., Toride, N., Bradford, S. A. and Pontedeiro, E. M., 2013, Exact analytical solutions for contaminant transport in rivers 1. The equilibrium advection-dispersion equation., Journal of Hydrology Hydromechanics 61(2), 146-160.

Wortmann, S., Vilhena, M. T., Moreira, D. M. and Buske, D., 2005, A new analytical approach to simulate the pollutant dispersion in the PBL., 39(12), 2171-2178.

Xu, Zh., Travis, J. R. and Breitung, W., 2007, Green's Function Method and Its Application to Verification of Diffusion Models of GASFLOW Code, Forschungszentrum Karlsruhe.

Yadav, R. and Jaiswal, D. K. J. , 2012, Two‐dimensional solute transport for periodic flow in isotropic porous media: an analytical solution., Hydrological Processes: An International Journal, 26(22), 3425-3433.

Yadav, R. and Kumar. L. J., 2019, Solute Transport for Pulse Type Input Point Source along Temporally and Spatially Dependent Flow., Pollution, 5(1), 53-70.

Yeh, G. T., 1981, AT123D: Analytical transient one-, two-, and three-dimensional simulation of waste transport in the aquifer system, Oak Ridge National Lab., TN (USA).

Zoppou, C. and Knight, J. J., 1999, Analytical solution of a spatially variable coefficient advection–diffusion equation in up to three dimensions., Applied Mathematical Modelling, 23(9), 667-685.