FLOOD01888

• County: Statewide
• Title: River Hydraulics
• Date: 10/15/1993
• Prepared By: US Army Corps of Engineers
• Floodplain - Doc Type: Educational/Technical/Reference Information

EM 1110-2-1416
15 Oct 93

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Inflow
Outflow

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25

30

5

10 152 20
Time (10 see)

.

Figure 5-21. Attenuation from a hypothetical dam break type flood routed 8,000 feet downstream through a
channel of unit width

explicit schemes is which changes are occurring to the
flows at reach boundaries. This can lead to a very ineffi-
cient solution. The time steps for implicit schemes are,
theoretically, dependent only on accuracy criteria and can
be many times larger than in explicit schemes. Implicit
models appear, further, to be generally more robust.

(2) Most of the successful models available today
use an implicit finite. difference scheme (Fread 1978,
1988; Shaffranek et al. 1981; Johnson 1982; U.S. Army
Corps of Engineers 1991b).

5-13. Diffusion Model

For some flow conditions the water surface slope and the
friction slope are nearly equal and the momentum equa-
tion becomes

5-28

dz
... -Sf
dX

(5-10)

This is the diffusion wave, or zero-inertia approximation.
Forces from all three sources are assumed to be in equi-
librium, so that the acceleration is zero. If the 8um of
local acceleration (a measure of unsteadiness) dQldt and
advective acceleration (a measure of nonunifonnity)
d(QV)ldX is small compared to the sum of weight (i.e.,
gravitational) and pressure components, this model is
capable of producing a simulation virtually as realistic as
the dynamic wave model. This is often the case for
flows at a low Froude number.

....

a. Assumptions. Local and advective accelerations
are often of similar magnitude and opposite sign; their
sum is typically smaller than either one alone.

.