Numerical investigation of solitary wave breaking over a slope based on multi-phase smoothed particle hydrodynamics

This study presents a numerical investigation of the solitary wave breaking over a slope by using the multi-phase smoothed particle hydrodynamics (SPH) method. Four different computational models are proposed to solve the gas-related far-field boundary conditions, and the model with the least disturbance to the internal flow field is selected. Since the artificial viscous coefficient can greatly affect the wave-breaking location, an empirical equation is fitted to quickly determine the optimal value of the artificial viscous coefficient. In addition, the turbulence model and three-dimensional effect on the wave breaking are discussed in this study. The results show that the present two-dimensional multi-phase SPH without a turbulence model can capture the macroscopic characteristics of the flow before the vortices convert to three dimensional flow structures caused by the wave breaking. Then, the processes of shoaling solitary wave breaking with different slopes and relative wave heights are simulated. Compared with the single-phase SPH, the multi-phase SPH is of great help in improving the prediction of wave breaking. A vortex similar to the Rankine Vortex is observed near the wave crest. Its intensity affects the pressure distribution of the gas, and its relative position to the wave crest is relevant to the energy transfer from the water to the gas. During the solitary wave propagating from deep water to shallow water, energy dissipation of gas and water shows four different stages. In the stage of energy dissipation, the gas can absorb the great energy from the water, which effectively dissipates the wave energy.