tsunami propagation modelling with...

Yusuke Oishi, James Southern

Fujitsu Laboratories of Europe

Computational Science at the Petascale and Beyond:

Challenges and Opportunities

Australian National University, 13 February 2012

Tsunami Propagation Modelling

With Fluidity

13 February 2012, Australian National University

Tsunami Propagation

Tsunami propagation simulations are generally

based on the shallow water equations or the

dispersive wave equations using finite

difference methods on structured meshes.

E.g., reported simulations of the Tohoku tsunami:

1 Copyright 2012 FUJITSU LABORATORIES OF EUROPE

Yamazaki et al. (2011, GRL)

Non-linear dispersive wave dx = ∼600-m - ∼3 km

Maeda et

al. (2011)

Linear shallow water

Fujii et

al. (2011)

Linear shallow water

Saito et al.

(2011, GRL)

Linear dispersive wave


3D Tsunami Simulations

Saito and Furumura

(2009, JGR):

Simulations based on

the 3D Navier Stokes

equations.

Accurately reproduce

dispersive waves.

But, on a uniform

structured mesh.


dx = 1km, dz = 200m, (Nx, Ny, Nz) = (1600, 2048, 110)

Saito and Furumura (2009, JGR)

Goal: Develop a highly accurate

tsunami model that runs on the most

powerful supercomputers using state-

of-the-art numerical methods.

Approach: Solve the 3D Navier-Stokes equations using finite

element methods on an unstructured mesh.


Unstructured Meshes


Unstructured mesh

(500 m ≤ dx ≤ 5 km)

Structured mesh

(dx = 500m)

http://maps.google.com


Layered Vertical Axis


z-coordinates σ-coordinates

Constant

number of

vertical layers


3D Tsunami Model

Run using the Fluidity-ICOM CFD code.

Galerkin finite element method.

P1DG-P2 elements (discontinuous linear u and

continuous quadratic p).

Unstructured tetrahedral mesh.

Linear solvers: GMRES + SOR for u, CG + AMG for p.

Crank-Nicolson time integration.


0

02

0

u

guuuu

νρ

p

t

0

p

uy

ux

ut

zyx

0　,0

n

tn

eueu

3-D Navier-Stokes

equations

Free surface

boundary

Bottom and

land boundaries


Ocean of Constant Depth

Compare to analytical solution for incompressible,

irrotational flow with constant depth.


3D NS model (3 vertical layers) Dispersive wave model

longer dispersive tail

delay

Shallow water model

at x = 100 km

no dispersive tail

early

depth: h = 4000 m

initial condition : kh = 3.14

x 0 250km

km) 8( λ


Example: Tohoku 2011



Comparing Simulations


3D NS model (3 layers) Dispersive wave model Shallow water model

t = 30 min

Close-up

8


Comparing to Real Data


21418

Fukushima

Iwate S

PG1

Initial wave height is according to Fujii et al. (2011). Observation data of ocean bottom pressure gauge are provided by

JAMSTEC (PG1) and NOAA/PMEL (21418), those of GPS buoy by MLIT and PARI. Bathymetry data J-EGG500 from JODC

and GEBCO are used.

Red: 3D NS

Gray: Observation


Computational Cost


Time required to simulate 1 minute of tsunami activity


Conclusions

A 3D unstructured mesh finite element model

tsunami model successfully simulated the Tohoku

tsunami using the Fluidity CFD package.

Dispersive waves were generated at the near-trench

region because of the short wavelength components of

the wave source and propagated to the east and west.

The 3D model is able to capture these short wavelength

(dispersive) waves – improving the accuracy of the wave

pattern near source.

Running full 3D simulations of large regions of

ocean requires very large compute resources.



Future Extensions

Multi-scale simulation consisting of:

Propagation.

Inundation processes, included by coupling a wetting/drying algorithm to 3D Navier-Stokes equations.

Larger computations.

Increase accuracy.

Model larger regions of the ocean/coastline.


Funke et al. (2011)

The 2011 Tohoku Earthquake Tsunami Joint

Survey Group (http://www.coastal.jp/ttjt)


Acknowledgements

Thanks to our collaborators at:

Applied Modelling and Computation Group, Imperial

College London.

Earthquake Research Institute, University of Tokyo.


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