Tsunami propagation simulations are very useful in both theoretical and application studies. Recent improvements in computer performance and the detailed bathymetry surveys in local- and global-scale make numerical simulations more feasible and reliable. This chapter treats the theoretical background and numerical schemes underlying tsunami propagation simulations. Since tsunami wavelength is usually greater than the sea depth, we approximate a 3-D equation of motion using 2-D tsunami equations. There are various kinds of tsunami equations according to the approximations. Hence, it is important to select appropriate tsunami equations depending on the situation and purpose of the simulation. Section 6.1 is an overview of various tsunami equations and introduces some results of the simulations. Section 6.2 derives the 2-D tsunami equations from the 3-D equation of motion by assuming long-wavelength wave propagation. We explain the linear long-wave equations, nonlinear long-wave equations, and linear dispersive equations. Section 6.3 illustrates the finite difference methods for numerically simulating the tsunami propagation across realistic bathymetry.
KeywordsLong-wave approximation Nonlinear long-wave equations Linear dispersive equations Nonlinear dispersive equations Finite difference method
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