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Chapter
Apr 26, 2012

A Staggered-Grid Scheme for the Advection-Dispersion Equation

Publication: World Environmental and Water Resource Congress 2006: Examining the Confluence of Environmental and Water Concerns

Abstract

A higher-order accurate numerical scheme is developed to solve the advection-dispersion equation. A staggered-grid system is introduced with the first-order spatial derivatives being approximated by the fourth-order accurate finite-difference scheme, thus keeping all truncation errors to a smaller order of magnitude than that of the dispersion term. The dispersion term, a second-order spatial derivative, is discretized by the second-order accurate finite-difference scheme. For the time derivative, the fourth-order accurate Adams predictor-corrector method is used. The numerical method is validated against available analytical solutions for a one-dimensional problem. The stability analysis is carried out using the Van Neumann method. It is shown that the proposed algorithm has a good stability property and there is no need to add a numerical dispersion term. As a result, the model can provide more accurate and stable results for long-term simulation. The model is demonstrated to be a useful and accurate modeling tool for a wide range of transport problems.

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Go to World Environmental and Water Resource Congress 2006
World Environmental and Water Resource Congress 2006: Examining the Confluence of Environmental and Water Concerns
Pages: 1 - 7

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Published online: Apr 26, 2012

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Chuanjian Man
Research Assistant and Ph. D. student, 207 Jarvis Hall, Department of Civil, Structural, and Environmental Engineering, State University of New York at Buffalo, Buffalo, NY 14260
Christina W. Tsai [email protected])
A.M.ASCE
Assistant Professor, 233 Jarvis Hall, Department of Civil, Structural, and Environmental Engineering, State University of New York at Buffalo, Buffalo, NY 14260 (. E-mail: [email protected])

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