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2D/3D HYBRID MODEL FOR TSUNAMI NUMERICAL SIMULATION

2D/3D HYBRID MODEL FOR TSUNAMI NUMERICAL SIMULATION. K.FUJIMA, National Defense Academy of Japan. Conventional Tsunami Numerical Model. Linear long wave equations for deep-sea region Nonlinear long wave equations for shallow-water region

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2D/3D HYBRID MODEL FOR TSUNAMI NUMERICAL SIMULATION

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  1. 2D/3D HYBRID MODEL FOR TSUNAMI NUMERICAL SIMULATION K.FUJIMA, National Defense Academy of Japan

  2. Conventional Tsunami Numerical Model • Linear long wave equations for deep-sea region • Nonlinear long wave equations for shallow-water region • Linear or nonlinear dispersive long wave equation is selected in some cases. • Finite Deference Method or Finite Element Method (FDM is popular in tsunami community.) • In the case of FDM, staggered grid is used in space, and leapfrog is in time-developing • Grid size in deep-sea region is 1-10 km, smallest grid is 2-50 m in dry-land area

  3. Conventional Method’s Shortcoming Governing equations = `Long Wave approximation’ • Three-dimensional complex flow around structures are not reproduced accurately. • e.g., surface velocity, bottom velocity, pressure around structure

  4. Non-hydrostatic-pressure 3D Model(Masamura, Fujima & Goto, 1996) • Euler’s equations of motion and continuity equation (div v=0) are solved without `long wave approximation’ • Strong nonlinearity and dispersion effect • Shortcoming=costly! (large grid number & iterative computation)

  5. Present Research • 2D/3D Hybrid model is developed. • Three-dimensional Reynolds-averaged Navier-Stokes equations are solved implicitly in the narrow region adjacent to the structure. • Two-dimensional conventional method is use for the wide region far from the structure.(explicit procedure)

  6. Computational Domain

  7. Governing Equations in 2D-Domain Which is extrapolated from 3D domain to 2D domain

  8. Governing Equations in 3D-Domain Note: Very small grid should be used in LES. It is not impossible for tsunami simulation to use such small grid. This simulation is not LES, although SGS model is used.

  9. SGS Model Note: Usual value c=0.2 provides similar results as experimental results. Vortex keeps too long time in case c=0, numerical results becomes too smooth in case c=0.4.

  10. Numerical Procedure(domain connection)

  11. Velocity Distribution at the Boundary of 3D Domain 3D model for whole domain(=target) uniform distribution of u present method boundary of domain

  12. Experimental Setup (1)

  13. Experimental Setup (2)

  14. Experimental Conditions • Still water depth, h=30cm • Incident wave height, H=2cm • Incident wave period, T=15s • Measurement duration=30s • Measurement items=velocity(u,w) and

  15. 3D Domain in Case a-d Note: If hybrid model results are similar to the results where 3D model is used in whole domain, it will prove the validity of domain-connection technique. Comparison of hybrid (or 3D) model results with experimental results and 2D model results will show the importance of 3D model.

  16. Grid Size and Computation Time

  17. Computed Mean Velocity Vector(Hybrid model)

  18. Computed Mean Velocity Vector(3D model for whole domain)

  19. Computed Velocity Vector in x-z Plain

  20. Velocity (u,w) Distribution (t=16s) Hybrid model Experiment

  21. Velocity (u,w) Distribution (t=22s) Hybrid model Experiment

  22. Velocity (u) Distribution (t=16s) Experiment Hybrid model Nonlinear SWW

  23. Velocity (u) Distribution (t=19s) Experiment Hybrid model Nonlinear SWW

  24. Velocity (u) Distribution (t=22s) Experiment Hybrid model Nonlinear SWW

  25. Velocity (u) Distribution (t=25s) Experiment Hybrid model Nonlinear SWW

  26. Velocity Distribution (t=22s) for the case with submerged breakwater

  27. Computed Surface Elevation (t=22s) for the case without submerged breakwater

  28. Computed Surface Elevation (t=22s) for the case with submerged breakwater

  29. Computed Tsunami Inflow Rate into Bay

  30. Maximum Bottom Shear Stressfor the case without submerged breakwater

  31. Maximum Bottom Shear Stressfor the case with submerged breakwater

  32. Force on structure provided by SWW model Force on structure provided by hybrid model Pressure on Submerged Breakwater

  33. Conclusions • Domain connection technique is successfully developed. • 2D/3D hybrid model is available for: • surface velocity --- diffusivity of drifts • bottom velocity --- bottom shear stress • pressure --- fluid force acting on structure

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