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E-proceedings of the 36th IAHR World Congress,28 June – 3 July,
2015, The Hague, the Netherlands
2
2
2
1 2 2 1 2 2
( )
( )
0
,
(1 ) ( ) (1 ) ( )
00.5
, ,0.5
y x
x x x
x y
y y y
gd z
gd z
x x
y
u
u
p u u v p v u v z
qqd
q gd q vq
q q v gd q
S Q F F (4)
where d is water depth; xq and q are discharges in x- and y-
directions respectively; z is the erodible bed thickness;
xF and F are convective fluxes in x- and y- directions
respectively; u and v are the velocity components in the x- andy-
directions respectively, g is the gravitational acceleration;
represents the intensity of interaction between flow andsediment
from weaker to strong as its value increases from 0 to 1, and p is
the porosity of bed material.
The friction slopes are estimated by using the Manning formula.
For Godunov-type finite volume method Eq. (3)becomes
1
1
1n n m L R n nQ Q F Q Q n l S Qt A
( , ) . ( ) (5)
The procedure for application of WENO scheme is explained in (Hu
& Shu, 1999; Zhu & Qiu, 2009, 2014). and Eq. (3)can be
written as2
1
1 1
13
mn n n
j j j j
Q Q t l F Q G t n S Q m A
( ( ( , )). ( )), (6)
3. NUMERICAL TESTS
3.1 Steady flow over a hump
Proposed model is tested for transcritical flow over hump on
fixed bed. The results in fig. 1 show excellent agreementwith
analytical solution satisfying the well-balancing and accuracy
requirements.
Distance (m)
W a t e r S u r f a c e E l e v a t i o n ( m )
0 5 10 15 20 250.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50 BedAnalyticalReconstruction (Jawahar& Kammath,2000)WENO
scheme
Figure 1.transcitical flow with shock on fixed bed over hump
3.2 Dam-break over an erodible sand bed
The experimental studies were performed at Civil Engineering
Department of UCL, Belgium (Spinewine & Zech, 2007).We
simulated our model for one case. The values of calibration
constant ( ), sediment porosity (p), and Manning’scoefficient (n)
are selected equal to 0.001, 0.47, and 0.0165, respectively, in
both cases. The domain was discretizedinto 1200 cells, and time
step of 0.001 was used to advance the solution. The results are
plotted after 0.25 s of dam-break in fig. 2. The comparison with
[10] shows closer agreement between WENO scheme output and
experimentalresults. At 0.25 s, both the reconstruction methods are
matching the experimental studies well; the bed erosion ispredicted
more precisely by WENO scheme. Performance of both the schemes in
capturing the position of wave front isequally satisfactory.
