Computational NAMI-DANCE complex in the problem of tsunami waves

Mathematical models applicable to the simulation of generation and propagation of tsunamis of different origin - underwater earthquakes, submarine landslides, meteotsunami - are described. The basic model is 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 PDE and leads to serious computational problems. We replace the physical dispersion with the numerical one using specific conditions for spatial and temporal steps. The numerical scheme is based on a Leap-Frog method. The equations are solved in spherical coordinates fixed to the rotating Earth by taking into account dissipative effects in the near-bottom layer with the use of NAMI-DANCE code. For tsunami waves of seismic origin, the initial conditions for hydrodynamic equations are found from the Okada solution of elastic equations describing the development of an earthquake...