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Generalized Analytical Solutions of The Advection-Dispersion Equation with Variable Flow and Transport Coefficients

Author

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  • Abhishek Sanskrityayn

    (Department of Mathematics, Post Graduate College, Ghazipur 233001, Uttar Pradesh, India)

  • Heejun Suk

    (Korea Institute of Geoscience and Mineral Resources, Daejeon 34132, Korea)

  • Jui-Sheng Chen

    (Graduate Institute of Applied Geology, National Central University, Taoyuan City 320, Taiwan)

  • Eungyu Park

    (Department of Geology, Kyungpook National University, Daegu 41566, Korea)

Abstract

Demand has increased for analytical solutions to determine the velocities and dispersion coefficients that describe solute transport with spatial, temporal, or spatiotemporal variations encountered in the field. However, few analytical solutions have considered spatially, temporally, or spatiotemporally dependent dispersion coefficients and velocities. The proposed solutions consider eight cases of dispersion coefficients and velocities: both spatially dependent, both spatiotemporally dependent, both temporally dependent, spatiotemporally dependent dispersion coefficient with spatially dependent velocity, temporally dependent dispersion coefficient with constant velocity, both constant, spatially dependent dispersion coefficient with spatiotemporally dependent velocity, and constant dispersion coefficient with temporally dependent velocity. The spatial dependence is linear, while the temporal dependence may be exponential, asymptotical, or sinusoidal. An advection–dispersion equation with these variable coefficients was reduced to a non-homogeneous diffusion equation using the pertinent coordinate transform method. Then, solutions were obtained in an infinite medium using Green’s function. The proposed analytical solutions were validated against existing analytical solutions or against numerical solutions when analytical solutions were unavailable. In this study, we showed that the proposed analytical solutions could be applied for various spatiotemporal patterns of both velocity and the dispersion coefficient, shedding light on feasibility of the proposed solution under highly transient flow in heterogeneous porous medium.

Suggested Citation

  • Abhishek Sanskrityayn & Heejun Suk & Jui-Sheng Chen & Eungyu Park, 2021. "Generalized Analytical Solutions of The Advection-Dispersion Equation with Variable Flow and Transport Coefficients," Sustainability, MDPI, vol. 13(14), pages 1-23, July.
    • Handle: RePEc:gam:jsusta:v:13:y:2021:i:14:p:7796-:d:593084
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    References listed on IDEAS

    as
    1. van Genuchten, M. Th. & Alves, W. J., 1982. "Analytical Solutions of the One-Dimensional Convective-Dispersive Solute Transport Equation," Technical Bulletins 157268, United States Department of Agriculture, Economic Research Service.
    2. Maria Grazia Stoppiello & Giusy Lofrano & Maurizio Carotenuto & Giacomo Viccione & Claudio Guarnaccia & Leonardo Cascini, 2020. "A Comparative Assessment of Analytical Fate and Transport Models of Organic Contaminants in Unsaturated Soils," Sustainability, MDPI, vol. 12(7), pages 1-24, April.
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    Cited by:

    1. Miglena N. Koleva & Lubin G. Vulkov, 2023. "Weak and Classical Solutions to Multispecies Advection–Dispersion Equations in Multilayer Porous Media," Mathematics, MDPI, vol. 11(14), pages 1-18, July.

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