ANUGA Workshop, 16 September 2008 How fine is fine enough? Convergence study of an ANUGA inundation model Leharne Fountain ANUGA – Present Applications

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

Documents

ANUGA Workshop, 16 September 2008 How fine is fine enough? Convergence study of an ANUGA inundation model Leharne Fountain ANUGA – Present Applications