Analytical Solution of Advection-Dispersion Equation with Spatially Dependent Dispersivity
Publication: Journal of Engineering Mechanics
Volume 143, Issue 11
Abstract
In the dispersion theory of solute transport in groundwater flow, the dispersion coefficient is regarded as proportional to the th power of groundwater velocity, where varies from 1 to 2. The present study derives an analytical solution of a one-dimensional (1D) advection-dispersion equation (ADE) for solute transport for any permissible value of . For a nonhomogeneous medium, groundwater velocity is considered as a linear function of space and analytical solutions are obtained for , 1.5, and 2.0. For , the dispersivity (ratio of dispersion coefficient and velocity) remains uniform, representing a homogeneous medium, while it varies with position in the finite domain (aquifer) for any other permissible value of representing the heterogeneity of the medium. From a hydrological point of view, the derived solutions are of significant interest and are of value in the validation of numerical codes. A generalized integral transform technique (GITT) with a new regular Sturm-Liouville problem (SLP) is used to derive analytical solutions in a finite domain. The analytical solutions elucidate the important features of solute transport with Dirichlet-type nonhomogeneous and homogeneous conditions assumed at the origin and at the far end of the finite domain, respectively. The first condition expresses a uniform continuous source of the dispersing mass. The analytical solutions are also compared with numerical solutions and are found to be in perfect agreement. The effect of a Peclet number on the solute concentration pattern is also investigated.
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Acknowledgments
The first and third authors acknowledge their gratitude to University Grants Commission, Government of India for financial and academic assistance in the form of Senior Research Fellowship. The authors are grateful to the learned reviewers for their minute and thorough review making the work of larger interest.
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Published In
Journal of Engineering Mechanics
Volume 143 • Issue 11 • November 2017
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©2017 American Society of Civil Engineers.
History
Received: Jan 20, 2017
Accepted: May 4, 2017
Published online: Aug 28, 2017
Published in print: Nov 1, 2017
Discussion open until: Jan 28, 2018
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