Computational NAMI-DANCE complex in the problem of tsunami waves

Abstract

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. In the case of meteotsunami, atmospheric factors are modeled by the external forces. The process of generation of tsunami waves of landslide origin is analyzed in the framework of a two-layer model with lower viscous layer modeling the motion of a submarine landslide. There are two kinds of boundary conditions: free wave passage through open boundaries (in straits, etc.) using linear shallow-water equations, and a full reflection on the coast or in near-shore area. The NAMI-DANCE code has been verified with several benchmarks. The difficulties of tsunami modelling associated with the lack of accuracy in the bottom bathymetry and land topography are mentioned. The use of the developed code for the analysis of tsunami action on the coasts and constructions is discussed.