The Use of the NAMI-DANCE Computational Complex on the Problem of Tsunami Waves

Mathematical models that are applicable to the simulation of the generation and propagation of tsunami waves from different sources, that is, underwater earthquakes, submarine landslides, and meteotsunamis, are described. The models are based on the well-known nonlinear shallow-water theory and its dispersion generalizations in two horizontal dimensions. Long wave dispersion related to the finiteness of water depth increases the order of the initial equations and, as a consequence, the time of computation. For this reason, physical dispersion in the investigations presented in this paper is replaced by numerical dispersion owing to a special choice of spatial and temporal steps. The numerical scheme for solving the shallow water equations is based on the leapfrog method. The equations are solved in spherical coordinates fixed to the rotating Earth with allowance for dissipative effects in the near-bottom layer with the use of the developed NAMI-DANCE code. For waves of seismic origin, the initial conditions for solving the hydrodynamic equations are taken from the solution of an elasticity theory problem to describe earthquake evolution (the Okada solution). In the case of a meteotsunami, atmospheric factors are taken into account as external forces and included in the right-hand sides of shallow water equations. Finally, generation of tsunami waves by submarine landslides is considered within the framework of a two-layer model with a lower viscous layer modeling the motion of the landslide. Two kinds of boundary conditions are used: free wave passage through open boundaries (in straits, etc.) using linear shallow-water equations and full reflection on the coast or in the near-shore area. Some test problems (benchmarks) on which the computational complex was verified are listed. The difficulties in the representation of tsunami characteristics due to bad data on the bottom bathymetry and topography of the land are mentioned. The possibility of using the developed code for the analysis of tsunami action on coasts and constructions is also discussed.