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Sand wave simulation on large domains

J. van den Berg R. van Damme

Department of EWI, NACMUniversity of Twente

RCEM 2005

J. van den Berg, R. van Damme Sand wave simulation on large domains

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ContextPhysical settingPractical relevanceOther research

ApproachProblem characteristicsGeneral applicabilityBenefitTechnique

ResultsFuture outlook

J. van den Berg, R. van Damme Sand wave simulation on large domains

OutlineContext

ApproachResults

Future outlook

Physical settingPractical relevanceOther research

Physical setting

J. van den Berg, R. van Damme Sand wave simulation on large domains

OutlineContext

ApproachResults

Future outlook

Physical settingPractical relevanceOther research

Physical setting

J. van den Berg, R. van Damme Sand wave simulation on large domains

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ApproachResults

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Physical settingPractical relevanceOther research

Practical relevance 09/19/2005 04:39 PMGoogle Maps

Page 1 of 2http://maps.google.com/

Drag the map with your mouse, or double-click to center.

Example searches:

Go to a location

"kansas city" try it

"10 market st, san francisco" try it

Find a business

"hotels near lax" try it

"pizza" try it

Get directions

To see all the details that are visible on the screen,use the "Print" linknext to the map.

courtesy Google maps

I Shipping routes

I Oil pipes

I Telecommunication cables

I Construction of artificialislands

I Off shore wind turbines

J. van den Berg, R. van Damme Sand wave simulation on large domains

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Physical settingPractical relevanceOther research

Other research

I Linear stability analysis (Hulscher, Gerkema, Besio)

I Trend fitting (Wust, Knaapen, probably numerous others)

I Numerical simulation (Nemeth)

J. van den Berg, R. van Damme Sand wave simulation on large domains

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Problem characteristicsGeneral applicabilityBenefitTechnique

Problem characteristics

Bottom shape Water flowfast time

Tidal averageslow time

I Two time scales

I Most computationeffort into flow

I Two consecutiveflows are alike

J. van den Berg, R. van Damme Sand wave simulation on large domains

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Problem characteristicsGeneral applicabilityBenefitTechnique

Why you should stay awake

I Many calculations

I Slightly different settings

I Profit

J. van den Berg, R. van Damme Sand wave simulation on large domains

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Problem characteristicsGeneral applicabilityBenefitTechnique

Applicability

Implicit solver, or time dependency harmonic

1.98 1.985 1.99

1.995 2

2.005 2.01

2.015 2.02

0 5 10 15 20

varia

ble

time

-1-0.8-0.6-0.4-0.2

0 0.2 0.4 0.6 0.8

1

0 5 10 15 20

varia

ble

time

-2-1.5

-1-0.5

0 0.5

1

0 5 10 15 20

varia

ble

time

J. van den Berg, R. van Damme Sand wave simulation on large domains

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Benefit

Compute small changes instead of whole trajectory

-1.5

-1

-0.5

0

0.5

1

0 5 10 15 20

varia

ble

time

J. van den Berg, R. van Damme Sand wave simulation on large domains

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Problem characteristicsGeneral applicabilityBenefitTechnique

How do we do that?

I Newton iterator from previous solution

I Sparse LU / GMRES

I Use previous LU as preconditioner for GMRES

J. van den Berg, R. van Damme Sand wave simulation on large domains

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Problem characteristicsGeneral applicabilityBenefitTechnique

On sparse LU

I Local discretisation in space

I Tactical ordering of the discrete equations

I Band matrix with little fill in during LU

I Nz < Nx gives small bandwidth

J. van den Berg, R. van Damme Sand wave simulation on large domains

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1 Wave

0 100 200 300 400 500 600!10

!5

0

5

10

15

20

J. van den Berg, R. van Damme Sand wave simulation on large domains

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1 Wave with migration

0 100 200 300 400 500 600 700!6

!4

!2

0

2

4

6

8

10

12

14

J. van den Berg, R. van Damme Sand wave simulation on large domains

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Wave field

! "!!! #!!! $!!! %!!! &!!! '!!! (!!! )!!!!"!

!&

!

&

"!

"&

J. van den Berg, R. van Damme Sand wave simulation on large domains

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Future outlook

I How do the variations evolve in time?

I Extensions: turbulence modelling, sediment transport

I Simplifications: better understanding of mechanism behindresidual flow

J. van den Berg, R. van Damme Sand wave simulation on large domains

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Acknowledgement

The research presented in this talk, is funded by the TechnologyFoundation STW, applied science division of NWO and thetechnology program of the Ministry of Economic Affairs (projectnumber TWO.5805: Modelling of spatial and temporal variationsin offshore sand waves: process-oriented vs stochastic approach).

J. van den Berg, R. van Damme Sand wave simulation on large domains

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If you ask for it

∂tu + u∂xu + w∂zu = Av∂2z u − g∂xζ + F (t) (1)

∂xu + ∂zw = 0 (2)

J. van den Berg, R. van Damme Sand wave simulation on large domains

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If you ask for it

Av∂zu = Su|z=h(x) (3)

w − u∂xh = 0|z=h(x) (4)

∂zu = 0|z=H+ζ(x ,t) (5)

w = ∂tζ + u∂xζ|z=H+ζ(x ,t) (6)

J. van den Berg, R. van Damme Sand wave simulation on large domains

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If you ask for it

B = α√|τb| [τb − λ1∂xh − λ2|τb|∂xh] (7)

τb = Av∂zu|z=h(x) (8)

∂th = −∂xB (9)

J. van den Berg, R. van Damme Sand wave simulation on large domains