With the improvement of Smoothed Particle Hydrodynamic (SPH), it has become one of most vigorous methods for breaking wave simulation. Recently we have developed an improved SPH method for simulating violent flow and two bodies interaction. The main features of this new method include the incompressible SPH method based the pressure Poisson equation, and it also gives a new scheme to deal with moving boundary. In this paper, this improved method will be applied for simulating waves and its impact with single floating body and two floating bodies, and the results are compared with experiment measurements.
The smoothed Particle Hydrodynamics (SPH) method is a meshless, purely Lagrangian technique which was originally developed by Lucy (1977), and Monaghan and Gingold (1977). While the WCSPH scheme has been successfully used for violent free surface flow, the stiff equation of state can result in large unphysical pressure fluctuations. These spurious oscillations in the pressure field can be mitigated by reducing the sound speed and relaxing the system at the same time. As a remedy for large unphysical pressure oscillations, Colagrossi and Landrini (2003) corrected the density calculation by renormalizing the density using Moving Least Square (MLS) density correction. They showed that, the correction improves mass area density consistency and also filters out pressure oscillations. They also found out that the density re-initialization procedure is beneficial with respect to energy conservation when it is used along with artificial viscosity. Molteni and Colagrossi (2009) have proposed a δ -SPH scheme by modifying the SPH equations and adding a proper artificial diffusive into the continuity equation in order to remove the spurious numerical high-frequency oscillations in the pressure field. However, these WCSPH issues need a very small time-step in order to resolve the artificial compressible equation. Another important improvement of pressure noisy is the scheme of weakly compressible SPH based on Riemann solver. Monaghan (1997) showed that the artificial viscosity is analogous to the terms constructed from signal velocities and jumps in variables across characteristics in the Riemann problem. Parchikov and Stanislav (2002) proposed a modified SPH method using a first order approximation of the acoustic Riemann solver, which does not require an artificial viscosity term for dissipation. Guo et al (2012) introduced the re-normalized approximation to the Riemann solver. According to the form of SPH based on Riemann solver, which is not uniform and some numerical techniques are still in open for discussion, different researchers may introduce different expressions, so SPH based on Riemann solver is not considered in this paper.
