by
Robert L. Runkel and Steven C. Chapra
Center for Advanced Decision Support for Water and Environmental Systems,
University of Colorado, Boulder
Several investigators have proposed solute transport models that incorporate the effects of transient storage. Transient storage occurs in small streams when portions of the transported solute become isolated in zones of water that are immobile relative to water in the main channel (e.g. pools, gravel beds). Transient storage is modeled by adding a storage term to the advection-dispersion equation describing conservation of mass for the main channel. In addition, a separate mass balance equation is written for the storage zone. Although numerous applications of the transient storage equations may be found in the literature, little attention has been paid to the numerical aspects of the approach. Of particular interest is the coupled nature of the equations describing mass conservation for the main channel and the storage zone. In the work described herein, an implicit finite difference technique is developed that allows for a decoupling of the governing differential equations. This decoupling method may be applied to other sets of coupled equations such as those describing sediment-water interactions for toxic contaminants. For the case at hand, decoupling leads to a 50 percent reduction in simulation run-time. Computational costs may be further reduced through efficient application of the Thomas algorithm. These techniques may be easily incorporated into existing codes and new applications in which simulation run-time is of concern.
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Beginning of document
Introduction
Governing Differential Equations
The Crank-Nicolson Method
Decoupling of the Stream and Storage Equations
Thomas Algorithm
Benchmark Runs
Conclusions
Acknowledgments
References