two dimensional simulation of a dam break wave propagation for the isolated building test case...
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Two Dimensional simulation of a Dam Break wave propagation for the isolated building test case
University of Pavia
Gabriella Petaccia
Impact Workshop...
Louvian La Neuve, November 2003
MATHEMATICAL MODEL
DISCRETIZATION
NUMERICAL SOLVER
Shallow water equations
Finite Volume
I order Upwind (Roe)
SOURCE TERMS SCHEMATIZATION
Bottom slope
Pointwise
(Valiani et al 2002)
Upwind-Mass balance equation
4
,100
kkkGw
V
VSzzgdVSxx
3
333
11
233
211
133
111
,
~1~1
~1~1
~1~1
eses
eses
eses
A
lt
i
ji
c
zhg
c
zhg
~2
~0~2
~
13
2
1
(Bermudez et al 1998)
Friction term3/7
112
ni
ni
nixn
ifh
qqnS
x
3/7
112
ni
ni
niyn
if h
qqnS
y
CFL 0.7
12945 elements
G1 G2
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0 5 10 15 20 25 30
t(s)
h(m
)
experimental data
pointwise
upwind
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0 5 10 15 20 25 30
t(s)
h(m
)
experimental data
pointwise
upwind
G4G3
G5 G6
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0 5 10 15 20 25 30t (s)
h (
m)
experimental data
pointwise
upwind
bil=0.5% upwind
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0 5 10 15 20 25 30
bil=0.1% pointwise
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0 5 10 15 20 25 30
t (s)
h(m
)
experimental data
pointwise
upwind
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0 5 10 15 20 25 30
t(s)
h(m
)
experimental data
pointwise
upwind
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0 5 10 15 20 25 30
t(s)
h(m
)
experimental data
pointwise
upwind
upwind
pointwise
VELOCITY FIELD T=1 s
t=1s
t=5s
t=10s
t=20s
NORM OF VELOCITY FIELD t= 1 s
NORM OF VELOCITY FIELD t= 2 s
NORM OF VELOCITY FIELD t= 5 s
NORM OF VELOCITY FIELD t= 10 s
Conclusions
•I order finite volume solver employing two different treatments of source terms has been applied to the isolated test case
•The comparisons between measured and simulated data is acceptable, the wave propagation is slower than in the experiments, the maximum water depth values are almost represented
•The upwind treatment seems more accurate in the gauges close to the building and reproduces more correctly the emptying phenomena
Thank you for your attention!!