Landslide-type tsunami modelling based on the navier - stokes equations
The paper presents a unified computing technology for all stages of landslide-type tsunami. The computing technology is based on the numerical solution of the Navier - Stokes equations for multiphase flows. The method of numerical solution of the Navier - Stokes equations uses a fully implicit algorithm. This algorithm removes stiff restrictions on the time steps and allows simulating a tsunami propagation in arbitrarily large water basins. The basic sampling equation formulas, coefficient types as well as the basic steps of the computational procedure are presented. The landslide is modeled by a single phase with its density and viscosity, which is separated by the interface from water and air phases. A parallel algorithm of the method implementation based on an algebraic multigrid method is proposed for the effective usage of the method to calculate the tsunami in large water areas. The multigrid method of implementation is based on algorithms of global level and cascading collection. These algorithms do not impose restrictions on the scale parallelization and allow the use of the proposed technology in petaflop class systems. It shows the possibility of simulating all the stages of the landslide-type tsunamis: generation, propagation and runup. The verification of the method is carried out by using the tests provided by the experimental data. The mechanism of bathymetric data accounting and the technology of constructing three-dimensional grid models are described. The results of the comparison with the non-linear dispersion theory are presented for the historical tsunami that resulted from a volcanic eruption on the island of Montserrat, the Caribbean. The results of this comparison are in good agreement.