Multi-layer non-hydrostatic free-surface flow model with kinematic seafloor for seismic tsunami generation

Earthquake induced tsunamis pose devastating threat to coastal communities worldwide. Accurate description of tsunami generation by kinematic fault rupture is of importance to investigate earthquake events and evaluate tsunami impacts. The paper develops a multi-layer non-hydrostatic model with a kinematic bottom boundary condition and conducts comprehensive validation to examine the model's capability in resolving seismic tsunami generation. The two-dimensional governing equations of the multi-layer non-hydrostatic free-surface flow system equipped with kinematic seafloor displacement is first introduced in Cartesian coordinates. A combined finite difference and finite volume scheme is utilized to discretize the governing equations with flow variables arranged on a staggered Arakawa C-grid. Application of pressure correction technique to the discretized formulations yields Poisson-type equations from which the non-hydrostatic pressure is solved for the next time step to complete the temporal integration. Based on existing analytical solutions, four groups of tsunami generation cases considering broad ranges of source parameters, including horizontal scale, rise time, and rupture velocity, are designed to demonstrate performance of the proposed non-hydrostatic model with one-, two-, and three-layers as well as the hydrostatic one. Comparison of 59 generation cases including extreme scenarios indicates the non-hydrostatic model performs better than the hydrostatic model in reproducing the entire waveform and predicting the maximum wave amplitude. High modeling accuracy can be achieved through incorporation of more layers. The proposed multi-layer non-hydrostatic model is a powerful tool for investigating earthquake source mechanisms and evaluating coastal tsunami hazards.