SPH modeling of solitary wave fissions over uneven bottoms

Abstract

The propagation of solitary wave in shallow water is investigated by using the Smoothed Particle Hydrodynamics (SPH) method. The present SPH model, which solves the weakly compressible Navier–Stokes equations and implements the wave absorbing scheme of Xu (2010) at downstream boundary, is first verified by the case of incident solitary wave propagating on a constant depth. A series of numerical experiments of solitary wave propagating over different bottom geometries are then conducted, which include the waves over a mild shelf or underwater steps with varied amplitude-depth ratios. The fission processes of both non-breaking and breaking solitary waves are discussed, numerical results of the free surface profiles and amplitude of the solitons show reasonable agreements with that of RANS model, as well as available experimental data. This paper demonstrates that the present method could reproduce the fission process with fairly good accuracy.