A Dirac-δ Function Notation for Source/Sink Terms in Groundwater Flow
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VIEW CORRECTIONPublication: Journal of Hydrologic Engineering
Volume 10, Issue 5
Abstract
The source/sink terms in groundwater flow are singularities that require special treatment in the numerical solution of a mathematical model. Except for the case of a point source, these singularities are not consistently defined in the governing partial differential equation or treated rigorously in the numerical solution of the governing equations. In this paper, we propose a consistent notation for handling the source/sink terms within the governing equation using the familiar Dirac- function notation for three-dimensional applications. We also present the domain integrals of these terms, similar to the ones that occur frequently in finite element solution of the mathematical model.
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Acknowledgments
The writers would like to thank Dr. Michael Ibison of Earthtech International, Inc. for his valuable comments and discussions.
References
Bear, J. (1979). Hydraulics of groundwater, McGraw-Hill, New York.
Charbeneau, R. J. (2000). Groundwater hydraulics and pollutant transport, Prentice Hall, Upper Saddle River, N.J.
Harris, J. W., and Stocker, H. (1998). Handbook of mathematics and computational science, Springer, New York.
Huyakorn, P. S., and Pinder, G. F. (1983). Computational methods in subsurface flow, Academic, New York.
Kusse, B., and Westwig, E. (1998). Mathematical physics: Applied mathematics for scientists and engineers, Wiley, New York.
Pinder, G. F., and Gray, W. G. (1977). Finite element simulation in surface and subsurface hydrology, Academic, New York.
Yeh, G. T. (1999). Computational subsurface hydrology, Kluwer Academic, Norwell, Mass.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 10 • Issue 5 • September 2005
Pages: 420 - 427
Copyright
© 2005 ASCE.
History
Received: Jul 11, 2003
Accepted: Feb 8, 2005
Published online: Sep 1, 2005
Published in print: Sep 2005
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