This paper presents a comparative numerical study for the water impact problems due to dropping of triangular wedges or ship sections. In the numerical investigation, both the dynamic mesh technique and immersed boundary method adopting fixed Cartesian grids have been adopted in order to conform to the motion of the structure. For the former, a multiple-phase solver with the volume of fluid for identifying the free surface is implemented. In the simulation using this method, both the compressible and incompressible solvers have been considered to explore the role of the compressibility. For the latter, an in-house immersed boundary method, in which a generalized equation is developed to govern the motion of different phases (air, water and solid) and a level-set method is adopted to identify the free surface & body surfaces. Different cases with different dropping speed have been considered in the investigation and the results are compared with the experimental data for the comparative study on the water impact problem.

The water entry is a complex, high-speed and nonlinear fluid-structure interaction problem covering many physical phenomena, such as the air trapping, free surface deformations, spray and jet flows. Significant impulsive pressure and slamming forces associated with the water entry problems lead to considerable hydro-elastic issues and, possibly, a severe damage of the offshore structure. Although this problem has been attracting the awareness of industrial and academic communities, the relevant understanding is still developing, in particular the role of the compressibility, aeration and hydro-elasticity, as revealed by recent experimental studies (e.g. Miyamoto and Tanizawa 1985; Okada and Sumi, 2000; Huera-Huarte et al. 2011; Ma et al, 2014, 2015; Mia et al, 2015).

Since Wagner (1932), attempts on deriving analytical solutions or empirical formula have been done to predict the slamming forces, e.g. Dobrovol'skaya (1969), Armand and Cointe (1986), Cointe (1991). Nevertheless, these analytical works were limited to simple-geometry or wedge-type bodies. In fact, the body shapes and impact angles play important roles on the impact pressure development and fluid-structure formation near the impact surface, as confirmed by the experimental observations, e.g. Okada and Sumi (2000) and Huera-Huarte et al. (2011). This limits the extension of the above-mentioned analytical works to bodies with more complex geometry, and therefore, initiated a fast growth of the numerical simulations on the water entry problems.