Smoothed particle hydrodynamics (SPH) is a particle-based numerical method that is well-suited to fluid flow problems where the computational domain becomes highly deformed. In this paper we use an SPH method to simulate the impact of a flat plate on a water surface, as carried out experimentally in the FROTH project at Plymouth University, Ma et al. (2016). A novel feature of the experiments was that, in order to mimic wave/structure impacts, the water was aerated by bubbling air from underneath the water surface. This created a non-homogeneous, compressible mixture. This implies that, for good quality simulations, very large numbers of particles are required, meaning in turn that parallelised code is required. Simulations have been carried out using single-phase SPH models, in both two and three spatial dimensions. The speed of the plate as it enters the water is specified from the experiments and data from this are used as boundary conditions for the SPH model. The results show generally good agreement in terms of free surface shape, pressure distributions, sound wave developments/reaction and pressure/time traces, but we note that maximum pressures as well as propagation and reaction of sound waves are highly dependent upon the sound speed specified within the weakly-compressible SPH model.
Smoothed particle hydrodynamic (SPH) has previously been successfully applied to the modelling of fluid flow, solid mechanics and fluid-solid interactions, especially when this involves large deformations. SPH is a fully Lagrangian method, which does not require the use of any mesh. It was invented by Lucy (1977) and Gingold & Monaghan (1977). Since then, the use of SPH has expanded in many areas of solid and fluid dynamics. Nowadays, the SPH method is widely used to simulate flows in hydro-engineering and geophysical applications.
In the Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) method, fluid pressure is related to particle density using a stiff equation of state. In the present work, WCSPH is discussed and used to simulate dropping a flat plate in to still water. The WCSPH method allows density fluctuations of around one percent by using a numerical speed of sound which is normally taken as ten times higher than the maximum fluid velocity.