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Tsunami benchmark cases: benchmark # 3

Tsunami benchmark cases: benchmark # 3. The third International workshop on long-wave runup models, June 2004. Stéphan Grilli, Enet Fran çois Department of Ocean Engineering, University of Rhode Island. Foreword.

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Tsunami benchmark cases: benchmark # 3

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  1. Tsunami benchmark cases: benchmark # 3 The third International workshop on long-wave runup models, June 2004 Stéphan Grilli, Enet François Department of Ocean Engineering, University of Rhode Island

  2. 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.

  3. Introduction • Benchmark parameters • Numerical model • Results • Conclusions

  4. Benchmark parameters: • Slide shape as function of time:

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

  6. Boundary conditions and geometry: • 1/10th slope • Constant depth region offshore • Absorbing piston offshore • Slide truncated at the bottom of the slope • 2 domains • L=40m, dmax=3.5m • L=80m, dmax=7.5m

  7. 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 Φt and Φtn are needed as BC for the two BEM problems needed for the second order time stepping:

  8. Kinematics:

  9. 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

  10. Discretization: • Total of 470 or 472 nodes and 383 or 384 elements • mid-interval elements (potential) • cubic splines (geometry) • Free surface:200 cubic boundary elements (dx= 0.2 or 0.4 m) • Slope: dx = 0.14 or 0.28 m

  11. 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)

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

  13. Results:

  14. Results:

  15. Results:

  16. Results:

  17. Results: Tsunami exits the domain

  18. 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

  19. 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.

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