Geoscience Reference
In-Depth Information
The discretizations of sediment transport, bed change, and bed material sorting
equations remain unchanged. The resulting equations include the dicretized sed-
iment transport equation (5.137), the discretized fractional bed change equation
(5.139), the discretized total bed change equation (5.133), the discretized bed mate-
rial sorting equation (5.135), and the implicitly treated sediment transport capacity
equation (5.141).
Flow equations (5.180)-(5.182) and sediment equations (5.133), (5.135), (5.137),
(5.139), and (5.141) can be solved in either iteratively or fully coupled form, as
described in the next subsection.
5.4.3 Solution of discretized coupled flow
and sediment transport equations
Iteratively coupled solution procedure
Iteratively coupled models can be found in Holly
et al
. (1990). In such models, all
the flow and sediment calculations are divided into two loops. The first loop is the
“flow loop,” which solves flow equations (5.180) and (5.181) using the latest esti-
mates of sediment discharge, bed elevation, and bed-material gradation. Eqs. (5.180)
and (5.181) are locally linearized by using
h
and
Q
as unknowns. The Manning
n
+
1
coefficient
n
n
+
1
, mixture density
A
b
,
i
+
1
in these two equations
are set as intermediate variables and replaced with the latest estimates
n
∗
,
ρ
1
, and bed change
i
+
ρ
i
+
1
, and
A
b
,
i
+
1
, which are determined using Eq. (5.182), related to sediment concentration,
and determined by the sediment model, respectively. The locally linearized equations
can be written as Eqs. (5.60) and (5.68), and solved using the algorithms described in
Section 5.2.2.
The second loop is the “sediment loop,” which solves Eqs. (5.133), (5.135), (5.137),
(5.139), and (5.141) to estimate sediment discharge, bed change, and bed-material gra-
dation. These equations can be solved using the direct solution method described in
Section 5.3.3.
To obtain a simultaneous solution of flow and sediment transport, these two loops
are coupled through the following iteration procedure:
(1) Load the imposed boundary conditions, such as mainstream and tributary water
and sediment inflows, and downstream water stage;
(2) Calculate water stage, flow discharge, and other flow parameters, using the latest
estimates of Manning
n
, flow density, and bed elevation;
(3) Compute sediment discharge, bed change, and bed-material gradation, using the
calculated flow conditions;
(4) Estimate new Manning
n
, flow density, and bed elevation, using the computed
flow and sediment quantities, and
(5) Repeat steps (2)-(4) iteratively until the successive estimates of bed elevation,
Manning
n
, etc., no longer change.
This iteratively coupled solution procedure can take into account interactions
between flow and sediment transport, indirectly giving a simultaneous solution. As a
simplified case, the flow and sediment models described in Sections 5.2.2 and 5.3.3
