Tsunami can be hydro dynamically considered as shallow water
(or long) waves, whose phase velocity is given as a
square root of product of water depth and the gravitational
acceleration. Because the ocean depth, or bathymetry,
is globally surveyed and mapped, the tsunami propagation
can be simulated using the actual bathymetry data.
A popular method of tsunami numerical simulation is a
finite-difference computation of equation of motion for
shallow-water waves (momentum conservation) and the
equation of continuity (mass conservation). For deep
ocean, a typical grid size is a few to several kilometers.
Near the coasts with shallow depths, non-linear effects
and bottom friction need to be included. In addition,
effects of local topography and bathymetry, such as reflection
or refraction, also play important role, hence the
smaller grid, typically with several tens of meter interval,
is adopted. For computation of tsunami inundation on
land, topographic data are also used with moving boundary
conditions.