Full Equations (FEQ) Model for the Solution of the Full, Dynamic
Equations of Motion for One-Dimensional Unsteady Flow in Open Channels
and Through Control Structures
Most open-channel flows of interest to hydraulic engineers, hydrologists, and planners are unsteady and can be considered to be one-dimensional (1-D). In unsteady flow, some aspect of the flow (velocity, depth, pressure, or another characteristic) is changing with time. In 1-D flow, longitudinal acceleration is significant, whereas transverse and vertical accelerations are negligible. Many problems involving 1-D unsteady flows have been approximated by assumption of steady flows (for example, constant peak discharges in flood-plain delineation studies) or piecewise steady flows, wherein storage-outflow relations are derived for channel reaches from a steady-flow hydraulic model and used in simple hydrologic-routing methods. Piecewise steady-flow analysis typically does not consider all the forces acting on the flow and only partially accounts for channel-storage effects. The approximate solutions for steady-flow and piecewise steady-flow analysis are adequate for certain simplified planning or design problems but are inadequate for many others (for example, streams with rapidly rising and falling stage, flat slopes, and broad flood plains where storage and acceleration effects could be substantial). No criteria are available to guide engineers and hydrologists as to when steady-flow methods are acceptable and when a complete unsteady-flow analysis is necessary. Further, problems such as tidally affected flows and sudden releases from power-generation stations require 1-D unsteady-flow analysis.
With the recent increases in the calculation speed and storage capabilities of computers, simulation of 1-D unsteady flow in a complex stream system with many hydraulic structures has become practicable. Runoff response to rainfall in urban areas is rapid, and streams throughout Illinois have relatively flat slopes and broad flood plains. Thus, engineers with the Illinois State government and rapidly urbanizing counties surrounding Chicago, became interested in applying unsteady-flow analysis for flood-plain delineation, flood forecasting, flood-control reservoir operation, and other applications. Because a wide variety of hydraulic structures in the stream network could be simulated in the Full EQuations (FEQ) model, this model was selected by the U.S. Geological Survey (USGS) and cooperating agencies for documentation and extensive testing (Ishii and Turner, 1997; Ishii and Wilder, 1993; Turner and others, 1996). The Illinois Department of Natural Resources, Office of Water Resources, and the County of Du Page, Department of Environmental Concerns, cooperated with the USGS and Linsley, Kraeger Associates to document model schematization, governing equations, mathematical solution procedures, numerical characteristics, and input description for FEQ.
Development of FEQ, a numerical tool for the solution of the flow-governing
equations for a system of interconnected channels, began in 1976. The structure
of the program was designed to represent the general structure of a stream
system, so the model is highly flexible and capable of efficiently simulating
a wide variety of stream systems. Among the many hydraulic structures represented
in the model are bridges, culverts, dams, level-pool reservoirs, spillways,
weirs, sluice gates, pumps, side weirs, expansions, contractions, drop
structures, and flows over roadways. Several options for the choice of
the governing equations are available. Wind forces on the stream surface
can be calculated and their effects on flow momentum simulated.