A new and efficient procedure for dispersive tsunami simulations on spherical coordinates based on a hyperbolic approach

When tsunamigenic events are simulated in deep to moderately deep waters, frequency dispersion effects may become mandatory. In the framework of dispersive systems, non-hydrostatic pressure type models have been shown to be able to describe weakly dispersive waves [2,3]. Although promising results begin to glimpse nowadays, dispersive solvers are still far from being robust, efficient and able to compute on a faster than real-time (FTRT) basis. The main difficulty that presents this type of systems is that at each time step a parabolic-elliptic problem has to be numerically solved and a high computational effort is required.

In [1] a novel weakly non-linear and weakly dispersive system that takes into account dispersive effects is presented. The main advantage is that the system is strictly hyperbolic and that any explicit numerical scheme can be applied to solve numerically the equations.

We will present new numerical results from an upgrade of the system presented in [1], considering curvature effects through a rewriting of the system in spherical coordinates. The numerical results will cover some standard field validation tests involving tsunami propagation waves. Besides, the explicit numerical scheme has been implemented exploiting the power of modern GPU architectures (CUDA). Then, numerical results along with some computational times will show that this numerical model opens a new line on tsunami simulation scenarios, using a new, efficient and accurate procedure to produce FTRT tsunami propagation including dispersive effects.

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

[1] C. Escalante, M. Dumbser, M. Castro, An efficient hyperbolic relaxation system for dispersive non-hydrostatic water waves and its solution
with high order discontinuous galerkin schemes, Journal of Computational Physics 394 (2019) 385 – 416.

[2] C. 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.

[3] Y. Yamazaki, Z. Kowalik, K. Cheung, Depth-integrated, non-hydrostatic model for wave breaking and run-up, Numerical Methods in Fluids
61 (2008) 473–497.