Geoscience Reference
In-Depth Information
where
p
∗
bk
,
P
is defined as
p
bk
,
P
, the fraction of size class
k
in the mixing layer of bed
material if
n
m
,
P
n
1
m
,
P
, and as the fraction of size class
k
in the second layer
+
z
b
,
P
+
δ
≥
δ
n
m
,
P
1
m
,
P
.
n
+
if
z
b
,
P
+
δ
<δ
6.2.3.2 Solution of discretized sediment transport equations
Fully decoupled model
Like the 1-D sediment transport model in Section 5.3, the depth-averaged 2-D sediment
transport model can be solved in a decoupled or coupled form. In the decoupled model,
the bed-material gradation in Eq. (6.56) is treated explicitly:
C
n
+
1
∗
p
bk
,
P
C
∗
n
+
1
q
n
+
1
b
p
bk
,
P
q
∗
n
+
1
=
,
=
(6.71)
k
,
P
k
,
P
∗
k
,
P
bk
,
P
The decoupled sediment transport model is usually decoupled from the flow model,
thus yielding a fully decoupled procedure for flow and sediment calculations. The
calculations in the fully decoupled model are executed as follows:
(1) Calculate the flow field;
(2) Calculate
C
n
+
1
∗
and
q
n
+
1
b
k
using Eq. (6.71);
k
∗
(3) Calculate
C
n
+
1
k
using Eq. (6.65);
(4) Calculate
q
n
+
1
bk
using Eq. (6.66);
(5) Determine
z
bk
and
z
b
using Eqs. (6.67) and (6.68);
(6) Calculate
p
n
+
1
bk
using Eq. (6.70);
(7) Update the bed topography using Eq. (6.69) and the bed-material gradations in
the subsurface layers;
(8) Return to step (1) for the next time step until a specified time is reached.
Semi-coupled model
In the semi-coupled model, the flow and sediment calculations are decoupled, but the
three components of the sediment model
−
sediment transport, bed change, and bed
material sorting
are coupled. To couple the sediment calculations, the bed-material
gradation in Eq. (6.56) is treated implicitly:
−
C
n
+
1
∗
p
n
+
1
bk
,
P
C
∗
n
+
1
q
n
+
1
b
p
n
+
1
bk
,
P
q
∗
n
+
1
k
,
P
=
k
,
P
=
,
(6.72)
k
,
P
∗
bk
,
P
The discretized suspended-load transport equation (6.65), bed-load transport
equation (6.66), bed change equations (6.67) and (6.68), bed material sorting equation
(6.70), and sediment transport capacity equation (6.72) need to be solved simultane-
ously through iteration. One iteration procedure is to set the bed-material gradation
p
bk
,
P
as the initial estimate for
p
n
+
1
bk
,
P
, and solve the above discretized equations, in the
sequence Eqs. (6.72), (6.65), (6.66), (6.67), (6.68), and (6.70), to obtain a new esti-
mate for
p
n
+
1
bk
,
P
. This is repeated until a convergent solution is reached. This iteration
procedure is simple, but the level of coupling among sediment transport, bed change,
