Towards a faster than real-time dispersive tsunami simulations

This work aims to develop and implement a numerical model, including dispersion suitable for tsunami simulations in the framework of TEWS. Therefore, including more physics but still computing much Faster than Real-Time (FTRT).

The main problem is that state-of-the-art dispersive models have an elliptical nature, instead of hyperbolic as the standard Shallow Water equations. In practice, this elliptic nature forces to solve a linear system at each time step of the simulation, with a remarkable decrease of the computational efficiency [2,3].

We have recently proposed a technique in which the elliptical model is approximated by a hyperbolic one, which preserves the dispersion relations [1]. As a result, any robust and efficient numerical scheme for hyperbolic systems can now be used to approximate it numerically.

We will present a latitude-longitude coordinate formulation to account for the effects of curvature, and we have proposed a dispersive model that is hyperbolic. We will show some simulations and comparisons in real test cases and computational times using GPU architectures that show promising results with excellent computational efficiency.

Acknowledgments: This research has been partially supported by the Spanish Government Research project MEGAFLOW (RTI2018-096064-B-C21), Universidad de Málaga, Campus de Excelencia Internacional Andalucía Tech and ChEESE project (EU Horizon 2020, grant agreement Nº 823844), https://cheese-coe.eu/

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Escalante, T. Morales, M. Castro, Non-hydrostatic pressure shallow flows: GPU implementation using finite volume and finite difference scheme, Applied Mathematics and Computation (2018) 631-659.

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