Geoscience Reference
In-Depth Information
equation (5.36) is discretized as
Q
n
+
1
tk
,
i
Q
n
+
1
t
Q
tk
,
i
+
1
−
Q
t
∗
k
,
i
+
1
L
t
,
i
+
1
1
−
p
m
)
A
bk
,
i
+
1
+
∗
k
,
i
+
1
(
1
−
=
θ
+
(
1
−
θ)
t
L
n
+
1
t
,
i
+
1
(5.139)
The total change in bed area is calculated using Eq. (5.133), the bed elevation
is updated using Eq. (5.134), and the bed-material gradations are determined using
Eqs. (5.135) and (5.136).
5.3.3.2 Solution of discretized unsteady sediment transport
equations
Decoupled sediment calculation
A decoupled procedure for solving the discretized sediment transport, bed change, and
bed material sorting equations can be established, if the bed-material gradation
p
bk
in
Eq. (5.35) is treated explicitly:
Q
n
+
1
t
p
bk
,
i
+
1
Q
∗
n
+
1
1
=
(5.140)
∗
k
,
i
+
tk
,
i
+
1
The sediment quantities at cross-section
i
+
1 are then obtained in the following
sequence:
(1) Compute
Q
n
+
1
t
1
using Eq. (5.140) with the known
p
bk
,
i
+
1
;
∗
+
k
,
i
(2) Calculate
Q
n
+
1
tk
,
i
1
using Eq. (5.138);
+
(3) Compute
A
bk
,
i
+
1
using Eq. (5.139);
(4) Calculate
A
b
,
i
+
1
using Eq. (5.133);
(5) Compute
p
n
+
1
bk
,
i
1
using Eq. (5.135), and
(6) Update the cross-section topography using Eq. (5.134), and calculate the bed-
material gradations in the subsurface layers.
+
Once the sediment discharges at the inlet have been determined using boundary con-
ditions, the forewater calculation of sediment transport can be performed cross-section
by cross-section, following the procedure laid out above. This decoupled procedure
is very simple but may be subject to non-physical phenomena, such as numerical
oscillation and negative bed-material gradation.
The decoupled sediment calculation is usually decoupled from the flow calculation.
Therefore, the entire flow and sediment calculations are fully decoupled.
Coupled sediment calculation
A coupled procedure for solving the discretized sediment equations described above
can be established, if the bed-material gradation
p
bk
in Eq. (5.35) is treated implicitly:
Q
n
+
1
t
p
n
+
1
bk
,
i
1
Q
∗
n
+
1
1
=
(5.141)
∗
k
,
i
+
+
tk
,
i
+
1
