Tsunami benchmark cases: benchmark

1
Tsunami benchmark cases benchmark 3
Stéphan Grilli, Enet François Department of Ocean
Engineering, University of Rhode Island

• The third International workshop on long-wave
  runup models, June 2004

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Foreword

• Due to lack of time, only case B was solved as
  this is the most demanding modeling case and is
  more likely to exhibit nonlinearities that the
  LSWE can't model but that the numerical FNPF
  solution accurately models.

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Introduction

• Benchmark parameters
• Numerical model
• Results
• Conclusions

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Benchmark parameters

• Slide shape as function of time

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Numerical Model

• Fully nonlinear potential flow higher-order
  2D-BEM model
• Grilli and Subramanya (1996)
• Grilli and Horrillo (1997)
• Grilli and Watts (1999)

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Boundary conditions and geometry

• 1/10th slope
• Constant depth region offshore
• Absorbing piston offshore
• Slide truncated at the bottom of the slope
• 2 domains
• L40m, dmax3.5m
• L80m, dmax7.5m

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Boundary conditions

• The deforming slide is modeled analytically and
  truncated either at 1 of maximum thickness delta
  (1 cm), or at the maximum depth of the
  discretization.
• Kinematics on the moving boundary calculated
  analytically.
• Both Ft and Ftn are needed as BC for the two BEM
  problems needed for the second order time
  stepping

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Kinematics
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Remarks

• Care was taken to have enough adaptive
  integration subdivision in the runup region which
  becomes very shallow.
• the runup point is forced to follow the slide
  shape by keeping x(t) as obtained from the Taylor
  series expansion providing the time stepping and
  calculating the corresponding elevation z
  analytically using the slide shape

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Discretization

• Total of 470 or 472 nodes and 383 or 384 elements
• mid-interval elements (potential)
• cubic splines (geometry)
• Free surface200 cubic boundary elements (dx 0.2
  or 0.4 m)
• Slope dx 0.14 or 0.28 m

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Time stepping

• Based on a mesh Courant condition and varies as
  (Lagrangian) nodes move
• average time step is about 0.015 or 0.02 s
• 900 time steps to compute up to t' 5s
• CPU time on a Mac G4 1.33 GHz laptop is 2-2.5 sec
  per time step (40 min)

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Accuracy

• Relative accuracy on Boundary fluxes is better
  than 5 10-8
• Volume conservation better than 5.10-6

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Results
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Results
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Results
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Results
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Results Tsunami exits the domain
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Conclusions

• The analytical LSWE solution provides a good
  prediction of tsunami shape given by the full
  FNPF solution only up to t'1 for the results
  provided.
• Larger differences with the FNPF solution occur
  at later time due to the depth limitation and to
  the proximity of the open BC

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References

• Grilli, S.T. and Subramanya, R. 1996. Numerical
  Modeling of Wave Breaking Induced by Fixed or
  Moving Boundaries. Computational Mechanics,
  17(6), 374-391.
• Grilli, S.T. and Horrillo, J. 1997 Numerical
  Generation and Absorption of Fully Nonlinear
  Periodic Waves. Journal of Engineering Mechanics,
  123 (10), 1060-1069.
• Grilli, S.T. and Watts, P. 1999 Modeling of waves
  generated by a moving submerged body.
  Applications to underwater landslides. Engng.
  Analysis Boundary Elemt., 23, 645-656.