Geoscience Reference
In-Depth Information
2. Governing Equations
Formulation of flow processes can be described by two-dimensional (2D)
St. Venant equations for shallow water problems, as follows:
H
+
H
,i
u
i
+
Hu
i,i
=0
,
(1)
u
i
+
u
j
u
i,j
−
ε
(
u
j,i
+
u
i,j
)
,j
+
g
(
H
+
z
)
,i
+
gn
2
√
u
k
u
k
H
4
/
3
K
|
W
|
W
i
u
i
−
+
fu
i
=0
,
(2)
H
where
i
(= 1
,
2) or
j
(= 1
,
2) are the subscript for horizontal co-ordinates
(=
x, y
)and
t
is the time. Differentiations with respect to (
x, y
)and
t
are denoted by subscripted comma and superscripted dot, respectively.
H
(
x, y, t
) is the water depth;
u
i
(
x, y, t
) is the depth averaged velocities;
ε
is the eddy viscosity coecient;
g
is the acceleration of gravity;
z
is the
bed elevation;
n
is the Manning coecient of roughness;
K
is the wind
stress coecient;
W
is the wind velocity; and
f
is the Coriolis parameter.
3. Generation of Finite Element Meshes and Solution
of the Inundation Processes by FEM
The model is based on 100 m grid-sized DEM topographic data of the study
area. And then refined, unstructured-triangular FEM meshes of 62,965
nodes and 124,997 elements were generated. Bed elevations of grids in
the DEM data are used to interpolate elevations of FEM nodes in the
floodplain domain, while more precise and new updated sound-bathymetry
data of the main rivers as bed elevations are utilized to interpolate FEM
nodes' elevations in the main rivers' domain. The weighted-residual of the
standard Galerkin FEM is applied to the 2D shallow water equations for
spatial discretization, and the selective lumping two-step explicit FEM is
employed for numerical integration in time. As for initial conditions, the
model is run with an assigned zero velocities and water surface elevations
with a linear slope based on observed water level data. At land bound-
aries, slip conditions are imposed along them, so that normal velocities of
nodes belonging to land boundaries are set to zero. Observed (or calcu-
lated) discharges of 12 tributaries around Tonle Sap Lake are set up at
ever-wet nodes which located in water-edge of the Lake in dry season, as
inflow-boundaries. Measured water levels as a function of time at Kratie
water level gauge are specified for the inflow of upstream conditions, while
those at Tan Chau and Chau Doc water level gauges are specified as for the
