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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
U.S. GEOLOGICAL SURVEY WATER-RESOURCES INVESTIGATIONS REPORT 96-4240
8.3 Initial Conditions
An initial value of flow and water-surface elevation must be known
at every node in the stream model before the unsteady-flow
computations can begin. These initial values are provided through
a steady-flow water-surface profile computation. A steady-flow
analog of the unsteady-flow governing equations for branches is
used in the steady-flow water-surface profile computations. Most
control structures are not represented in these computations. An
estimate of the initial conditions is obtained from the
steady-flow computations so that the unsteady-flow
computations can start. Consequently, an option is provided for
holding the boundary conditions and the simulation time constant
while initial values of water-surface height are computed. This
option is called frozen time. If the frozen-time option is
selected by the user, the changes in water-surface height and flow
that would take place over a time step are computed, but then the
simulation time is reset to the starting time. Normally, only a
few frozen time steps must be computed to dissipate transient
conditions resulting from the change from steady flow to unsteady
flow. If the frozen-time option is selected, a maximum of nine
frozen time steps will be computed. In most cases, nine frozen
time steps will suffice to reduce computational transitions;
however, for simulations of
tidally affected flows or streams with many control structures,
the computational transients can be particularly strong. In these
cases, boundary conditions may have to be held constant (using a
hypothetical period of constant conditions) during the start of
the unsteady-flow computations (after frozen time) for a period
long enough to
dissipate the transients induced by the approximate initial
condition.
The equations for the steady-flow analysis are not presented
here because they are a special case of the
governing equations for unsteady flow. A subcritical solution
to the governing equations is sought, but (as outlined in
section 2.2) a subcritical solution may not exist. If a
subcritical solution cannot be computed, then the iterative
solution procedure will fail and computations will stop in FEQ.
The user must then determine why supercritical flow results.
Is the distance step too long or is the slope too steep for
subcritical flow? Details of this determination are given in
section 13.
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Last modified: Wed Nov 12 13:45:17 CST 1997