The impact and motion characteristics of high-speed projectiles during water entry in waves are critical factors to be considered in the design and development process. In this study, a numerical wave tank is established using the smoothed particle hydrodynamics (SPH) method combined with the periodic boundary technique. The six degrees of freedom (6-DOF) motions of the projectile are calculated using the Quaternion method, and the SPH model combined with the Quaternion method is adopted to simulate the water entry process of a high-speed projectile in waves. Firstly, the water entry processes of the cuboid and projectile in static water are simulated and compared with numerical and experimental data to verify the accuracy of SPH simulation of impact and motion characteristics based on the Quaternion method. The SPH method with the periodic boundary technique is then used to establish a numerical tank under wave conditions and simulate the water entry process of the projectile in waves with different phase angles. The simulation results are compared with reference data from previous studies, which shows that the SPH model combined with the periodic boundary technique and Quaternion method can accurately predict the water entry process of high-speed projectiles in waves. This study can provide technical support for the design and optimization of high-speed projectiles in engineering applications.

High-speed hydrodynamics and its corresponding complex fluid-structure interactions (FSI) are challenging topics associated with naval architecture and ocean engineering, typically characterized by large deformations, moving boundaries, strong convection and multiple fluid media. Since traditional mesh-based numerical methods possess limited ability to accurately simulate such strongly nonlinear problems, it is imperative to develop meshless numerical schemes with high fidelity and robustness to tackle this dilemma. As one of the most promising truly meshless methods, smoothed particle hydrodynamics (SPH) shows apparent advantages in high-speed hydrodynamics problems thanks to its Lagrangian nature. In the present paper, the attention is particularly focused on the latest advances of several SPH techniques with respect to the following high-speed hydrodynamics problems: vessel-induced waves and wakes, the water entry process of projectiles, and underwater explosion and its resulting structural damage; in addition, the future prospects of SPH are provided in the last part of the paper.