Depth-integrated, non-hydrostatic model with grid nesting for tsunami generation, propagation, and run-up

Tsunamis generated by earthquakes involve physical processes of different temporal and spatial scales that extend across the ocean to the shore. This paper presents a shock-capturing dispersive wave model in the spherical coordinate system for basin-wide evolution and coastal run-up of tsunamis and discusses the implementation of a two-way grid-nesting scheme to describe the wave dynamics at resolution compatible to the physical processes. The depth-integrated model describes dispersive waves through the non-hydrostatic pressure and vertical velocity, which also account for tsunami generation from dynamic seafloor deformation. The semi-implicit, finite difference model captures flow discontinuities associated with bores or hydraulic jumps through the momentum-conserved advection scheme with an upwind flux approximation. The two-way grid-nesting scheme utilizes the Dirichlet condition of the non-hydrostatic pressure and both the horizontal velocity and surface elevation at the inter-grid boundary to ensure propagation of dispersive waves and discontinuities across computational grids of different resolution. The inter-grid boundary can adapt to bathymetric features to model nearshore wave transformation processes at optimal resolution and computational efficiency. A coordinate transformation enables application of the model to small geographic regions or laboratory experiments with a Cartesian grid. A depth-dependent Gaussian function smoothes localized bottom features in relation to the water depth while retaining the bathymetry important for modeling of tsunami transformation and run-up. Numerical experiments of solitary wave propagation and N -wave run-up verify the implementation of the grid-nesting scheme. The 2009 Samoa Tsunami provides a case study to confirm the validity and effectiveness of the modeling approach for tsunami research and impact assessment. Copyright 2010 John Wiley & Sons, Ltd.