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

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