Solution of 1D Space Fractional Advection-Dispersion Equation with Nonlinear Source in Heterogeneous Medium
Publication: Journal of Engineering Mechanics
Volume 146, Issue 12
Abstract
Fractional derivatives, owing to their nonlocal behavior, are well suited for modeling the fate of contaminants in a heterogeneous medium. This study develops the mathematical formulation and the solution of a one-dimensional (1D) fractional flux advection-dispersion equation (FFADE) for an increasing or decreasing nonlinear source of contamination in the permeable region. In the proposed model, the first-order space derivative is replaced with the fractional derivative of order () () in a Riemann-Liouville sense. The model assumes a spatiotemporally varying dispersion and seepage velocity, constant dispersion and uniform seepage velocity, linear dispersion and linear seepage velocity, and quadratic dispersion and linear seepage velocity, exhibiting various levels of medium heterogeneity. Initially, the medium is considered to be polluted with solute concentration and spatially varying specific concentration . The approximate solution to the model is obtained by the modified Adomian decomposition method. It is remarked that change in the medium’s heterogeneity alters the peak of solute concentration, and the presence or absence of advection in the solute transport process significantly affects the concentration distribution. The obtained results are validated with field data available in the literature. The obtained solutions may be used to predict solute concentration in the permeable region from penetrating contaminant sources situated at any place along a vertical plane perpendicular to the direction of, for example, groundwater flow.
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Data Availability Statement
All code generated and used during the study that supports the findings is proprietary in nature and may only be provided with restrictions.
Acknowledgments
The authors are thankful to the Science Engineering Research Board, Department of Science and Technology, for its financial support under Research Project EMR 2016/001628. The authors are also thankful to the editor and reviewers for their constructive comments, which helped improve the quality of the paper.
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Published In
Journal of Engineering Mechanics
Volume 146 • Issue 12 • December 2020
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Apr 9, 2019
Accepted: Jul 30, 2020
Published online: Sep 30, 2020
Published in print: Dec 1, 2020
Discussion open until: Feb 28, 2021
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