An efficient numerical solution of the transient storage equations for solute transport in small streams

Water Resources Research
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Abstract

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% 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.

Additional publication details

Publication type Article
Publication Subtype Journal Article
Title An efficient numerical solution of the transient storage equations for solute transport in small streams
Series title Water Resources Research
DOI 10.1029/92WR02217
Volume 29
Issue 1
Year Published 1993
Language English
Publisher American Geophysical Union
Contributing office(s) Toxic Substances Hydrology Program
Description 5 p.
First page 211
Last page 215