Geoscience Reference
In-Depth Information
Because of its special link between bed change and sediment discharge, Eq. (5.123)
can be easily solved using the finite volume method on a staggered grid, in which
sediment discharge is stored at cell faces and bed change is stored at cell centers.
Integrating Eq. (5.123) over the control volume in Fig. 4.14 yields
p
m
)
z
b
,
P
(
1
−
t
x
P
+
q
t
,
e
−
q
t
,
w
=
0
(5.127)
where
q
t
,
e
and
q
t
,
w
are the sediment discharges at faces
e
and
w
and can be determined
using the first-order upwind scheme or the QUICK scheme introduced in Section 4.3.1.
The calculations at each time step are executed as follows: (a) compute flow using
the steady or unsteady flow model introduced in Section 5.2; (b) determine sediment
discharge using an empirical sediment transport formula; (c) calculate bed change
using one of Eqs. (5.124)-(5.127); and (d) update channel geometry. In addition,
bed material sorting is also calculated for non-uniform sediment transport. This is
introduced in Sections 5.3.2 and 5.3.3.
5.3.2 1-D quasi-steady non-equilibrium sediment
transport model
5.3.2.1 Representation of hydrographs
Denote the characteristic length, time, and velocity of fluvial processes in an open chan-
nel as
U
, the time-derivative terms in the St. Venant equations
(5.1) and (5.2) and sediment transport equations (5.27), (5.28), and (5.34) can be omit-
ted. Therefore, the fluvial processes can be simulated using a step-wise quasi-steady
model. As demonstrated in Fig. 5.14, the continuous time series of flow discharge,
water stage, and sediment discharge are represented by step functions that are con-
structed with the corresponding representative quantities over a suitable number of
,
T
, and
U
.If
T
/
Figure 5.14
Representation of hydrographs in quasi-steady model.
