ANUGA Workshop, 16 September 2008 How fine is fine enough? Convergence study of an ANUGA inundation...

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


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!)


Part I: Is ANUGA scaleable?


• Transform the Okushiri model to true-scale and verify– Elevation model– Domain & polygons– Input wave

• Compare model output with that from original model

Methodology


Time-series comparisons






Part II: Does ANUGA converge?


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


Depth

Elevation

Stage

Stage = Depth - Elevation

Offshore:

Stage = Depth + Elevation

Onshore:

Stage

Elevation

Depth

MSL

Terminology


Elevation


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


R = 640


R = 1.25


Input wave


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


Run time vs No. of Triangles

100

1000

10000

100000

1000 10000 100000 1000000

Number of triangles

Ru

n t

ime

(s)


Results: Time domain


Polygons and gauges

Ch 9

Ch 7

Ch 5

a

b

c

d

e

1 2 3 4 5


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



-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



-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


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


Results: Spatial domain


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)


Maximum depth


2.5


5


10


20


40


80


160


320


640


Depth at constant times


t = 200 s


t = 200 s


t = 250 s


t = 250 s


t = 300 s


t = 300 s


t = 350 s


t = 350 s


t = 400 s


t = 400 s


t = 450 s


t = 450 s


640


Difference in maximum depth

Difference in depth at t = constant

t


Part III: How fine is fine enough?


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


Determining risk

• Maximum extent of inundation

• Offshore wave height

• Maximum flow speeds


Max extent of inundationR = 1.25

Max extent of inundationR = 640

Coastline(elevation = 0)

Maximum extent of inundation


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

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ANUGA Workshop, 16 September 2008 How fine is fine enough? Convergence study of an ANUGA inundation...

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