Geoscience Reference
In-Depth Information
suspended-load concentration from 3-D to 2-D and then to 1-D subdomains using
these four conditions, but the reverse conversion is not unique. To solve this problem,
a common practice is to locate the interfaces at nearly straight prismatic channels or
regions far away from hydraulic structures so that the following approximations are
acceptable: the water level can be assumed to have a uniform lateral distribution; the
depth-averaged flow velocity can be determined by Eq. (6.17); the unit transport rates
of bed load and suspended load can be given by Eq. (6.63) at the interface from 1-D
to 2-D subdomains; and the local flow velocity can be assumed to follow the log or
power law and the local suspended-load concentration can be determined using the
Rouse or Lane-Kalinske distribution along the depth at the interface from 2-D to 3-D
subdomains. In addition, if the 2-D and 3-D grid points do not match at the interface,
interpolation and conservative correction are needed in the conversion of 2-D and
3-D quantities.
8.2.3 Calculation procedures
For steady flow in a channel shown in Figs. 8.10(a) and (b), the flow discharges
in all reaches are readily known. For simplicity, only subcritical flow is considered
here. Thus, the calculation may be conducted reach by reach from downstream to
upstream, with the water level at the outlet of each reach provided by the adjacent
downstream reach and the lateral distribution of depth-averaged flow velocity at the
inlets of 2-D and 3-D reaches determined by Eq. (6.17). However, for unsteady flow
in such a channel, the hydrodynamic equations in all reaches are related and should
usually be solved in a coupled manner. Conditions (8.9)-(8.11) should be satisfied at
the interfaces.
For sediment transport in a channel shown in Figs. 8.10(a) and (b) under both
steady and unsteady conditions, the calculation is conducted reach by reach from
upstream to downstream, with the upstream reach providing boundary conditions for
the downstream reach. Conditions (8.13)-(8.16), (8.18), and (8.19) should be satisfied
at the interfaces.
For flow and sediment transport in a wide water body shown in Fig. 8.10(c), the
governing equations in all subdomains should usually be solved together with con-
ditions (8.9), (8.10), (8.13), and (8.14) at the interfaces. In addition to the solution
procedures in individual component models, an iteration loop among subdomains
should be introduced.
The computational time steps allowed by numerical stability in 1-D, 2-D, and 3-D
models are usually different. Therefore, the overall time step should be carefully
selected. One choice is to use the shortest time step allowed by all component models.
The other choice is to use different time steps in different component models and con-
vert the quantities at interfaces in different times by interpolation. The former choice
is less efficient, whereas the latter choice is cumbersome for fully coupling unsteady
1-D, 2-D, and 3-D models.
8.2.4 Examples
Coupled 1-D/2-D/3-D models have been applied in numerous case studies. For exam-
ple, McAnally
et al
. (1986) used a mixed 2-D/3-D model to study the salinity intrusion
