Geoscience Reference
In-Depth Information
3. Method of Analysis
3.1.
Governing equations
In this study, the computational area is divided into three parts: river chan-
nel, hillside area, and flood-prone area, as shown in Fig. 3.
In the river channel, one-dimensional (1D) unsteady flow analysis using
the characteristics method is applied following to Inoue
et al
.
1
:
∂A
∂t
+
∂Q
∂x
=
q,
1
g
∂u
∂t
+
u
∂u
∂x
+
∂h
∂x
=
s
0
−
s
f
,
g
where
A
is cross-sectional area of flow,
Q
the discharge,
q
the lateral inflow
from unit length of the
x
-direction,
u
the velocity averaged over cross-
section,
s
0
the river bed slope,
s
f
the friction slope, and
g
is the gravitational
acceleration.
In the hillside area, runoff analysis using the kinematic wave method
integrating surface and subsurface flow
2
is applied:
∂h
∂t
+
1
∂
(
qb
)
∂x
=
r
cos
θ,
b
k
sin
θ
γ
q
=
h
(0
<h<γD
)
,
q
=
√
sin
θ
n
γD
)
m
+
k
sin
θ
γ
(
h
−
h
(
h
≥
γD
)
,
Hommyo River basin
discharge at the
upstream end
hillside area
runoff model using
kinematic wave
method integrating
surface and sub-
surface flow
flood-prone area
two-dimensional
inundation flow
model using
unstructured meshes
river channel
one-dimensional
unsteady flow
model using
characteristics
method
overtopping
runoff
discharge
Drainage
through
pump
stations
water level at the
downstream end
Fig. 3.
Framework of the model.
