Ocean Dynamics

, Volume 61, Issue 9, pp 1261-1285

First online:

Quadtree-adaptive tsunami modelling

  • Stéphane PopinetAffiliated withNational institute of Water and Atmospheric Research Email author 

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The well-balanced, positivity-preserving scheme of Audusse et al. (SIAM J Sci Comput 25(6):2050–2065, 2004), for the solution of the Saint-Venant equations with wetting and drying, is generalised to an adaptive quadtree spatial discretisation. The scheme is validated using an analytical solution for the oscillation of a fluid in a parabolic container, as well as the classic Monai tsunami laboratory benchmark. An efficient database system able to dynamically reconstruct a multiscale bathymetry based on extremely large datasets is also described. This combination of methods is successfully applied to the adaptive modelling of the 2004 Indian ocean tsunami. Adaptivity is shown to significantly decrease the exponent of the power law describing computational cost as a function of spatial resolution. The new exponent is directly related to the fractal dimension of the geometrical structures characterising tsunami propagation. The implementation of the method as well as the data and scripts necessary to reproduce the results presented are freely available as part of the open-source Gerris Flow Solver framework.


Saint-Venant Godunov Wetting and drying Well balanced Indian Ocean tsunami Okushiri tsunami Fractal dimension Terrain reconstruction