Numerical technology for landslide tsunami simulations based on Navier-Stokes equations - Kozelkov, Andrey Sergeevich (Computational Continuum Mechanics, 2016)
The paper presents an integral technology simulating all phases of a landslide-driven tsunami. The technology is based on the numerical solution of a set of Navier-Stokes equations for multi-phase flows. The numerical algorithm uses a fully implicit approximation method, in which the equations of continuity and momentum conservation are coupled through implicit summands of pressure gradient and mass flow. The method we propose removes strict constraints on the timestep and makes it possible to simulate tsunami propagation to arbitrarily large distances. The landslide origin is simulated as an individual phase being a Newtonian fluid with its own density and viscosity and separated from the water and air phases by an interface. The paper presents the basic equation discretization formulas and expressions for coefficients and describes the main steps of the computational procedure. To enable simulations of tsunami propagation across wide water areas, we propose a parallel technology implementation algorithm that employs an algebraic multi-grid method. The multi-grid method implementation is based on the global and cascade collection algorithms, which impose no limitations on the paralleling scale and make this technology applicable to petascale systems. We demonstrate the possibility of simulating all phases of a landslide-driven tsunami, including its generation, propagation and uprush. The technology has been verified against the problems supported by experimental data. The paper describes the mechanism of incorporating bathymetric data to simulate tsunamis in real water areas of the world ocean. Results of comparison with the non-linear dispersion theory, which demonstrated good agreement, are presented for the case of a historical tsunami of volcanic origin on the Montserrat island in the Caribbean Sea.