Geoscience Reference
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The bed changes at the inlet and outlet can be calculated using Eq. (6.67). The bed
change along a vertical rigid wall may be extrapolated from the values at adjacent
internal points. The bed change at the water edge near a sloped bank or island may be
set to zero, because the flow depth is almost zero there; however, the bank or island
may deform (collapse) due to the effect of gravity.
Bed-material gradations at boundary points can be calculated using Eq. (6.70) in
analogy to those at internal points.
6.2.4 Examples
Two examples are cited here to demonstrate the verification and application of the
depth-averaged 2-D model.
Case 1. Erosion in a basin due to clear water inflow
The erosion process in a rectangular basin due to clear water inflow from a narrow
channel experimentally investigated by Thuc (1991) was numerically simulated by
Minh Duc et al . (2004) and Wu (2004). The basin was 5m long and 4m wide, con-
nected with a 0.2m wide and 2m long channel in the upstream and a 1.2m wide
and 1.0m long channel in the downstream. The basin bed was covered with a 0.16m
thick layer of fine sand. The sand had a settling velocity of 0.013m
s 1 . The inflow
·
s 1 , and the water depth at the outlet was
0.15m during the experiment. The two simulations used similar flow models based
on the finite volume method, with slight difference in pressure correction as described
in Section 6.1.3.1. Both applied the non-equilibrium transport model of bed load and
suspended load described in Section 6.2.1; however, Minh Duc et al . used the sediment
exchange model (2.128), the saltation step length for bed-load adaptation length, and
the van Rijn formulas for sediment transport capacity, while Wu used the sediment
exchange model (2.132), the sand dune length for bed-load adaptation length, and
the Wu et al . (2000b) formulas for sediment transport capacity. The computational
meshes in the basin consisted of 62
·
velocity in the upstream channel was 0.6m
62 nodes, and the grid spacing around the basin
centerline was refined in each mesh. The time step for sediment calculation was 5 sec
×
Figure 6.5 Simulated flow field at 4 hr (Wu, 2004).
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