Sand wave simulation on large domains

Transcription

1 Sand wave simulation on large domains J. van den Berg R. van Damme Department of EWI, NACM University of Twente RCEM 2005

2 Physical setting Practical relevance Other research Problem characteristics General applicability Benefit Technique

3 Physical setting Physical setting Practical relevance Other research

4 Physical setting Physical setting Practical relevance Other research

5 Google Maps Practical relevance 09/19/ :39 PM To see all the details that are visible on the screen,use the "Print" link next to the map. Physical setting Practical relevance Other research Shipping routes Oil pipes Telecommunication cables Construction of artificial islands Off shore wind turbines Drag the map with your mouse, or double-click to center. courtesy Example searches: Google maps 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

6 Other research Physical setting Practical relevance Other research Linear stability analysis (Hulscher, Gerkema, Besio) Trend fitting (Wüst, Knaapen, probably numerous others) Numerical simulation (Németh)

7 Problem characteristics Problem characteristics General applicability Benefit Technique Bottom shape fast time Water flow Two time scales Most computation effort into flow slow time Tidal average Two consecutive flows are alike

8 Why you should stay awake Problem characteristics General applicability Benefit Technique Many calculations Slightly different settings Profit

9 Applicability Problem characteristics General applicability Benefit Technique variable Implicit solver, or time dependency harmonic time variable time variable time

10 Benefit Problem characteristics General applicability Benefit Technique Compute small changes instead of whole trajectory variable time

11 How do we do that? Problem characteristics General applicability Benefit Technique Newton iterator from previous solution Sparse LU / GMRES Use previous LU as preconditioner for GMRES

12 On sparse LU Problem characteristics General applicability Benefit Technique Local discretisation in space Tactical ordering of the discrete equations Band matrix with little fill in during LU N z < N x gives small bandwidth

13 1 Wave !5!

14 1 Wave with migration !2!4!

15 Wave field "& "! &!!&!"!! "!!! #!!! $!!! %!!! &!!! '!!! (!!! )!!!

16 How do the variations evolve in time? Extensions: turbulence modelling, sediment transport Simplifications: better understanding of mechanism behind residual flow

17 Acknowledgement The research presented in this talk, is funded by the Technology Foundation STW, applied science division of NWO and the technology program of the Ministry of Economic Affairs (project number TWO.5805: Modelling of spatial and temporal variations in offshore sand waves: process-oriented vs stochastic approach).

18 If you ask for it t u + u x u + w z u = A v 2 z u g x ζ + F (t) (1) x u + z w = 0 (2)

19 If you ask for it A v z u = Su z=h(x) (3) w u x h = 0 z=h(x) (4) z u = 0 z=h+ζ(x,t) (5) w = t ζ + u x ζ z=h+ζ(x,t) (6)

20 If you ask for it B = α τ b [τ b λ 1 x h λ 2 τ b x h] (7) τ b = A v z u z=h(x) (8) t h = x B (9)