Modeling of propagation tsunami waves via lattice Boltzmann method

Abstract

We present an efficient implementation of the Lattice Boltzmann method (LBM) for the numerical simulation of the propagation of long ocean waves (e.g., tsunamis), based on the Nonlinear Shallow Water (NSW) wave equation. The Lattice Boltzmann Equation (LBE) method is an alternative numerical scheme for the description of incompressible hydrodynamics. The LBE method has potential to serve as an efficient solver for incompressible flows in complex geometries. In the present study, we propose nonlinear shallow water equations for irrotational surface waves for the case of complex bottom elevation. Nowadays shallow water equations have become the model of choice for operational tsunami modeling including the propagation zone estimation. Several test-cases are presented to highlight the added value of the new model. Some implications to tsunami wave modeling are also discussed. The numerical results are found to be in excellent agreement with theory.