Taitoko, an advanced code for tsunami propagation, developed at the French Tsunami Warning Centers. (English) Zbl 1493.76070
Summary: This paper presents the new version of the operational code used at the Tsunami Warning Centers in French Polynesia and in mainland France. This nested multigrid code solves either the nonlinear shallow water or the weakly nonlinear Boussinesq equations in a spherical or Cartesian coordinates system. The objective is to simulate the propagation of tsunamis both in the context of tsunami early warning and in the context of research. The originality of this code is to simulate the tsunami propagation through a series of nested grids in which the numerical scheme is specified by the user. Three standard finite-difference methods and two finite volume schemes are available to take into account the dispersive nature of waves or to capture flow discontinuities. The performance of the five numerical schemes has been assessed through idealized 1D and 2D test cases. The convergence rate with grid refinement is evaluated for three of these tests. Diffusion and dispersion of the five schemes are evaluated through the 1D far-field propagation in a channel of constant depth. Finally, two-dimensional simulations of the 2011 Japanese tsunami are performed considering a homogeneous tectonic source. Coastal inundation is simulated in the bay of Kamaishi where run-up heights reached 10 m. The ability of the five schemes to propagate trans-Pacific tsunamis is evaluated through comparisons of time series between simulations and observations at DART buoys. In the context of tsunami early warning, numerical results show that standard finite-difference methods reproduce most of the observed time gauges and that numerical errors associated to these schemes are acceptable.
MSC:
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
| 76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
| 86A05 | Hydrology, hydrography, oceanography |
Keywords:
finite difference method; finite volume method; tsunami propagation; nonlinear shallow water equations; Boussinesq approximation; frequency dispersionReferences:
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