Approximate Analytical Solution to Groundwater Velocity Variance in Unconfined Trending Aquifers in the Presence of Complex Sources and Sinks
Publication: Journal of Hydrologic Engineering
Volume 14, Issue 10
Abstract
In this paper, we present a stochastic-analytical approach for uncertainty modeling in two-dimensional, statistically nonuniform groundwater flows. In particular, we develop simple closed-form expressions that can be used to predict the variance of Darcy velocities caused by random small-scale heterogeneity in hydraulic conductivity. The approach takes advantage of the scale disparity between the nonstationary mean and fluctuation processes and invokes an order-of-magnitude analysis, enabling major simplifications and closed-form solutions of the nonstationary perturbation equations. We demonstrate the accuracy and robustness of the derived closed-form solutions by comparing them with the corresponding numerical solutions for a number of nonstationary flow examples involving unconfined conditions, transient conditions, complex trends in mean conductivity, sources and sinks, and bounded domains.
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Acknowledgments
The research described in this paper was partially funded by the National Science Foundation (Grant No. NSFCISE-0430987).
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Published In
Journal of Hydrologic Engineering
Volume 14 • Issue 10 • October 2009
Pages: 1119 - 1125
Copyright
© 2009 ASCE.
History
Received: Jun 16, 2008
Accepted: Feb 24, 2009
Published online: Feb 25, 2009
Published in print: Oct 2009
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