Tsunami Propagation Modelling With...
Transcript of 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:
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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
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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.
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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.
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Unstructured Meshes
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Unstructured mesh
(500 m ≤ dx ≤ 5 km)
Structured mesh
(dx = 500m)
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Layered Vertical Axis
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z-coordinates σ-coordinates
Constant
number of
vertical layers
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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.
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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
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Ocean of Constant Depth
Compare to analytical solution for incompressible,
irrotational flow with constant depth.
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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
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Example: Tohoku 2011
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Comparing Simulations
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3D NS model (3 layers) Dispersive wave model Shallow water model
t = 30 min
Close-up
8
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Comparing to Real Data
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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
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Computational Cost
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Time required to simulate 1 minute of tsunami activity
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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.
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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.
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Funke et al. (2011)
The 2011 Tohoku Earthquake Tsunami Joint
Survey Group (http://www.coastal.jp/ttjt)
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Acknowledgements
Thanks to our collaborators at:
Applied Modelling and Computation Group, Imperial
College London.
Earthquake Research Institute, University of Tokyo.
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