1-D numerical models - Computational River Dynamics - page 178

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1 ), the characteristics C + > 0 and C − <

0.
As shown in Fig. 5.2(a), a C + characteristic curve enters from outside to the solution
domain through the inlet, and a C − characteristic curve enters through the outlet.
To determine the flow properties at the inlet and outlet, information from each char-
acteristic curve entering from outside has to be provided by a boundary condition.
Therefore, a boundary condition should be specified at each of the two boundaries.
Usually, a time series of flow discharge is specified at the inlet, and a time series of
water stage or a stage-discharge rating curve is imposed at the outlet.
For supercritical flow ( Fr

For subcritical flow ( Fr = U <

1), two characteristics are positive: C + > 0 and C − > 0.

As shown in Fig. 5.2(b), both C + and C − characteristic curves enter from outside
through the inlet, and no characteristic curve enters through the outlet. Therefore,
two boundary conditions should be imposed at the inlet, and none is required at the
outlet.

>

Figure 5.2 Characteristic curves of dynamic wave model at inlet and outlet boundaries.

Similarly, it can be derived that the diffusive wave model requires two boundary
conditions, which are specified at the inlet and outlet, respectively. The kinematic wave
model requires only one boundary condition, which is often specified at the inlet.
In addition, the initial water stage and flow discharge in the solution domain should
be given for an unsteady flow simulation.

5.1.1.3 Manning roughness coefficient
The Manning roughness coefficient n accounts for the effect of bed roughness on the
flow field, and its determination is essential to the accuracy of the calculated flow,
sediment transport, and bed change. For a movable bed with sediment grains and
bed forms as roughness elements, the Manning n can be evaluated using one of the
empirical formulas introduced in Section 3.3.3. However, the Manning n generally
depends on a number of factors, including channel size, cross-section shape, channel
alignment, channel meandering and curvature, surface roughness, bed forms, obstruc-
tions, vegetation, sediment transport, temperature, and seasonal changes. Therefore,
it is suggested that the Manning n should be calibrated, if gauged water surface profiles
and high water marks are available; otherwise, the Manning n values in similar stream
conditions should be used as guides. There are several references available for deter-
mining the Manning n , e.g., Chow (1959), Fasken (1963), Barnes (1967), and Hicks
and Mason (1991).
In the case of reservoir sedimentation, because the water stage is raised significantly,
bank roughness becomes important and should be considered in the flow calculation.
Usually, the Manning n values on banks and bed are different. In addition, due to