Numerical predictions of water–air wave slam using incompressible–compressible smoothed particle hydrodynamics

The high-speed impact between a body and water is an important practical problem, whether due to wave impact on a structural deck or wall, or due to a moving body such as a ship or aircraft hitting water. The very high pressures exerted are difficult to predict and the role of air may be significant. In this paper, numerical simulations are undertaken to investigate the impact of a rigid horizontal plate onto a wave crest and, in the limit, onto a flat water surface. A two-phase incompressible–compressible smoothed particle hydrodynamics (SPH) method for water and air, respectively, is applied where the water phase imposes kinematics on the air phase at the air–water interface and the air phase imposes pressures on the water at the interface. Results are compared with experimental measurements undertaken using a drop rig positioned over a wave flume so that a horizontal plate impacts the water surface in free flight. Numerical predictions of impact pressure are quite accurate; air is shown to have a significant cushioning effect for impact on to flat water and this reduces for waves as the ratio of wave height to wavelength increases.