Contaminant transport analysis under non-linear sorption in a heterogeneous groundwater system

Autor: Rashmi Radha, Rakesh Kumar Singh, Mritunjay Kumar Singh
Jazyk: angličtina
Rok vydání: 2022
Předmět:
Zdroj: Applied Mathematics in Science and Engineering, Vol 30, Iss 1, Pp 736-761 (2022)
Druh dokumentu: article
ISSN: 2769-0911
27690911
DOI: 10.1080/27690911.2022.2138867
Popis: In this study, a one-dimensional non-linear advection–dispersion equation subject to spatial–temporal dependent advection and dispersion coefficients is solved for a heterogeneous groundwater system. The non-linearity of the governing equation is based on the Freundlich and Langmuir sorption isotherms. The groundwater flow is considered to vary exponentially with time. Also, a generalized theory of the dispersion coefficient is used for extensive study of the model problem. The approximate solutions of the model problem are obtained in a semi-infinite and finite heterogeneous media by employing the Crank–Nicolson scheme. The exact solutions are obtained in both domains by the Laplace transform technique subject to linear sorption isotherm and non-transient flow conditions. Further, various graphical solutions are obtained using MATLAB scripts to examine the contaminant transport behaviour. For quantitative evaluation of the proposed model, a root mean square (RMS) error is computed. Overall, the results show that RMS error of the approximate solutions with respect to the exact solutions is within acceptable limits (less than 5%) for different combinations of discretization parameters. The robustness of the proposed model suggests its better suitability for modelling groundwater transport phenomena under the consideration of a non-linear sorption isotherm.
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