A finite element numerical model is developed for the modeling of coupled
surface-water flow and ground-water flow. The mathematical treatment of subsurface
flows follows the confined aquifer theory or the classical Dupuit approximation for
unconfined aquifers whereas surface-water flows are treated with the kinematic wave
approximation for open channel flow. A detailed discussion of the standard approaches to
represent the coupling term is provided. In this work, a mathematical expression similar
to Ohm's law is used to simulate the interacting term between the two major hydrological
components. Contrary to the standard approach, the coupling term is incorporated
through a boundary flux integral that arises naturally in the weak form of the governing
equations rather than through a source term. It is found that in some cases, a branch cut
needs to be introduced along the internal boundary representing the stream in order to
define a simply connected domain, which is an essential requirement in the derivation of
the weak form of the ground-water flow equation. The fast time scale characteristic of
surface-water flows and the slow time scale characteristic of ground-water flows are
clearly established, leading to the definition of three dimensionless parameters, namely, a
Peclet number that inherits the disparity between both time scales, a flow number that
relates the pumping rate and the streamflow, and a Biot number that relates the
conductance at the river-aquifer interface to the aquifer conductance.
The model, implemented in the Bill Williams River Basin, reproduces the observed
streamflow patterns and the ground-water flow patterns. Fairly good results are obtained
using multiple time steps in the simulation process.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/615700 |
| Date | 01 1900 |
| Creators | Vionnet, Leticia Beatriz, Maddock, Thomas, III, Goodrich, David C. |
| Contributors | Department of Hydrology & Water Resources, The University of Arizona |
| Publisher | Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ) |
| Source Sets | University of Arizona |
| Language | en_US |
| Detected Language | English |
| Type | text, Technical Report |
| Source | Provided by the Department of Hydrology and Water Resources. |
| Rights | Copyright © Arizona Board of Regents |
| Relation | Technical Reports on Hydrology and Water Resources, No. 97-020 |
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