A two phase Smoothed Particle Hydrodynamics method is developed to simulate the violent deformation of the free surface and the formation of the cavity induced by the two dimensional wedge entering water. The flow field of water and air are computed simultaneously. A non-reflection boundary treatment for SPH method is proposed to remove reflection of pressure wave against the solid boundaries of computational domain. The water jet generated at the early stage of water entry and the cavity induced by the free surface sealing are reproduced for the case of the vertical water entry of a wedge. The computational pressure distribution and the velocity field can be obtained. Numerical results agree well with the experimental data in literature to verify the two phase SPH method and the boundary treatment approach. It turns out that the cavity evolves with significant deformation of the cavity surface.
Water entry is part of the general fluid-structure impact problem in the field of marine hydrodynamics. Following the pioneer work by von Karman, lots of works have been carried out on hydrodynamic impact on the body entering water from air through the free surface and the evolution of the cavity running with the body. Considering a water entering wedge as a model for studying on slamming, the first complete solution was obtained by Dobrovol'skaya(1969) for a two-dimensional wedge based on potential flow theory and, then, Zhao and Faltinsen(1993) studied theoretically the same problem using a refined procedure. Wu, Sun and He(2004) carried out a numerical and experimental study of this problem more carefully for the early stage of water entry. The Smoothed Particle Hydrodynamics method (referring as SPH method) is attractive on simulating the violent deformation of the free surface and breaking wave, e.g. Oger et al (2006).