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ANUGA Workshop, 16 September 2008
How fine is fine enough?Convergence study of an ANUGA inundation model
Leharne Fountain
ANUGA – Present Applications and Future Potential
Geoscience Australia, 16-17 September 2008
ANUGA Workshop, 16 September 2008
Research questions: a tale in three parts
• Is ANUGA really scaleable? (We hope so!)
• Does ANUGA really converge? (We hope so!)
• At what spatial mesh resolution/s will ANUGA perform optimally? (Good question!)
ANUGA Workshop, 16 September 2008
Part I: Is ANUGA scaleable?
ANUGA Workshop, 16 September 2008
• Transform the Okushiri model to true-scale and verify– Elevation model– Domain & polygons– Input wave
• Compare model output with that from original model
Methodology
ANUGA Workshop, 16 September 2008
Time-series comparisons
ANUGA Workshop, 16 September 2008
Time-series comparisons
ANUGA Workshop, 16 September 2008
Time-series comparisons
ANUGA Workshop, 16 September 2008
Part II: Does ANUGA converge?
ANUGA Workshop, 16 September 2008
Methodology
• Define model– Use contour-based interior polygons
• Vary mesh resolution– Alter max triangle area by factor of 2
• Measure convergence– Time-series comparison
order of convergence– Spatial comparison
ANUGA Workshop, 16 September 2008
Depth
Elevation
Stage
Stage = Depth - Elevation
Offshore:
Stage = Depth + Elevation
Onshore:
Stage
Elevation
Depth
MSL
Terminology
ANUGA Workshop, 16 September 2008
Elevation
ANUGA Workshop, 16 September 2008
Contour-based interior polygons
-25 m-10 m
-5 m
1m
r = 1600R 2000m2 –
1,024,000m2
r = 80R100m2 –
51,200m2
r = 8R10m2 – 5120m
2
r = 3.2R4m2 –
2048m2
r = R1.25m2
– 640m2
ANUGA Workshop, 16 September 2008
R = 640
ANUGA Workshop, 16 September 2008
R = 1.25
ANUGA Workshop, 16 September 2008
Input wave
ANUGA Workshop, 16 September 2008
Model statistics
Resolution
(max tr. area)
Approx tr. side length
No. of triangles
Computation time (hh:mm:ss)
1.25 1.58 474,312 19:20:26
2.5 2.24 238,897 6:05:54
5 3.16 120,808 2:17:46
10 4.47 62,070 0:41:14
20 6.32 32,913 0:14:49
40 8.94 18,488 0:07:14
80 12.65 11,469 0:04:18
160 17.88 8,301 0:03:16
320 25.30 6,909 0:02:49
640 35.78 6,373 0:02:44
ANUGA Workshop, 16 September 2008
Run time vs No. of Triangles
100
1000
10000
100000
1000 10000 100000 1000000
Number of triangles
Ru
n t
ime
(s)
ANUGA Workshop, 16 September 2008
Results: Time domain
ANUGA Workshop, 16 September 2008
Polygons and gauges
Ch 9
Ch 7
Ch 5
a
b
c
d
e
1 2 3 4 5
ANUGA Workshop, 16 September 2008
Gauge comparisons - ch5
-5
0
5
10
15
20
0 50 100 150 200 250 300 350 400 450
Time (s)
Sta
ge
(m)
ch5_obs
1.25
2.5
5
10
20
40
80
160
320
640
ANUGA Workshop, 16 September 2008
Gauge comparisons - ch7
-5
0
5
10
15
20
0 50 100 150 200 250 300 350 400 450
Time (s)
Sta
ge
(m)
ch7_obs
1.25
2.5
5
10
20
40
80
160
320
640
ANUGA Workshop, 16 September 2008
Gauge comparisons - ch9
-5
0
5
10
15
20
0 50 100 150 200 250 300 350 400 450
Time (s)
Sta
ge
(m)
ch9_obs
1.25
2.5
5
10
20
40
80
160
320
640
ANUGA Workshop, 16 September 2008
L2 norm (difference from highest resolution) vs resolution (log-log scale)
-0.5
0
0.5
1
1.5
0 0.5 1 1.5 2 2.5 3
Log(Max triangle area)
log
(L2)
Order of convergence = 1
n
iiRRl
1
210
2 )(log
ANUGA Workshop, 16 September 2008
Results: Spatial domain
ANUGA Workshop, 16 September 2008
Spatial mesh performance
• Maximum depth over whole simulation
• Depth at constant times
• Each of the 9 models subtracted from highest resolution model (R=1.25)
ANUGA Workshop, 16 September 2008
Maximum depth
ANUGA Workshop, 16 September 2008
2.5
ANUGA Workshop, 16 September 2008
5
ANUGA Workshop, 16 September 2008
10
ANUGA Workshop, 16 September 2008
20
ANUGA Workshop, 16 September 2008
40
ANUGA Workshop, 16 September 2008
80
ANUGA Workshop, 16 September 2008
160
ANUGA Workshop, 16 September 2008
320
ANUGA Workshop, 16 September 2008
640
ANUGA Workshop, 16 September 2008
Depth at constant times
ANUGA Workshop, 16 September 2008
t = 200 s
ANUGA Workshop, 16 September 2008
t = 200 s
ANUGA Workshop, 16 September 2008
t = 250 s
ANUGA Workshop, 16 September 2008
t = 250 s
ANUGA Workshop, 16 September 2008
t = 300 s
ANUGA Workshop, 16 September 2008
t = 300 s
ANUGA Workshop, 16 September 2008
t = 350 s
ANUGA Workshop, 16 September 2008
t = 350 s
ANUGA Workshop, 16 September 2008
t = 400 s
ANUGA Workshop, 16 September 2008
t = 400 s
ANUGA Workshop, 16 September 2008
t = 450 s
ANUGA Workshop, 16 September 2008
t = 450 s
ANUGA Workshop, 16 September 2008
640
ANUGA Workshop, 16 September 2008
Difference in maximum depth
Difference in depth at t = constant
t
ANUGA Workshop, 16 September 2008
Part III: How fine is fine enough?
ANUGA Workshop, 16 September 2008
How fine is fine enough?
• What is the purpose of our model?– Determine risk– Make decisions in response to risk
• How does the mesh resolution affect these decisions?
• Balance computational expense and accuracy
ANUGA Workshop, 16 September 2008
Determining risk
• Maximum extent of inundation
• Offshore wave height
• Maximum flow speeds
ANUGA Workshop, 16 September 2008
Max extent of inundationR = 1.25
Max extent of inundationR = 640
Coastline(elevation = 0)
Maximum extent of inundation
ANUGA Workshop, 16 September 2008
Summary
• ANUGA is scaleable
• ANUGA achieves first order convergence
• Spatial & temporal investigation of mesh resolution provides more information about mesh performance
• Consider purpose of model, data requirements & computational expense in selection of optimal resolution