A high-order solver for simulating tsunami genesis and propagation induced by highly time-dependent earthquake ground motion

To improve the understanding of tsunami generation and propagation mechanisms and to enable more rigorous coastal hazard assessments, numerical simulation has become an indispensable tool. In most tsunami models, seismic dynamics are simplified as an instantaneous displacement of the seafloor; however, atypical events such as the 2018 Palu tsunami have highlighted the limitations of this assumption and demonstrated that seismic dynamics can play a critical role when rupture propagation occurs at speeds comparable to tsunami wave propagation. Fully coupled three-dimensional fluid–solid interaction models can account for these effects, but their computational cost makes them impractical for the parametric studies required in risk analysis.

In this work, we investigate the influence of dynamic seafloor motion on tsunami generation using a simplified modeling framework based on modified Saint-Venant equations. We propose a two-dimensional nonlinear spectral solver founded on the Fourier Continuation (FC) method, which provides high-order resolution of the governing equations while effectively eliminating numerical dispersion. This property significantly improves long-range accuracy and makes the method particularly well suited for capturing the multiple spatial and temporal scales involved in seismogenic tsunami modeling. Compared to commonly used finite-volume or finite-difference approaches, which can often suffer from dispersion errors that accumulate during propagation that require costly refinement, the spectral FC-based solver offers a fast (FFT-comparable), accurate, and low-cost alternative.

The solver has been validated against a range of analytical and experimental benchmarks, demonstrating its relevance for high-fidelity tsunami simulations. New results further highlight its capability to model both the generation and propagation of tsunamis driven by dynamically evolving seismic sources obtained from 3D rupture simulation software facilitated by discrete and spectral element methods. These results extend previous one-dimensional studies to a fully two-dimensional framework and open new perspectives for the efficient and accurate numerical investigation of tsunami hazards.