Comparative study of single-phase and multi-phase consistent δ＋-SPH models with a boundary shield technique for simulating violent sloshing flows

Violent sloshing flows under various conditions including wave traveling, entrapped air bubbles/pockets and high-frequency tank motions are investigated through comparative simulations using single-phase and multi-phase consistent δ+-SPH models. To enhance numerical robustness in violent sloshing simulations, a boundary shield technique (BST) is proposed to prevent unphysical penetration at solid walls. The consistent δ+-SPH results are validated against analytical solutions and experimental data. Numerical results show that the multi-phase consistent δ+-SPH simulations accurately capture pressure evolution and complex liquid–gas interface dynamics, particularly in cases involving entrapped air bubbles. For sloshing cases without significant air entrainment, the single-phase model achieves comparable accuracy with much lower computational cost. Moreover, for cases where air bubbles are entrapped but rapidly breaking up, such as the sloshing under high-frequency tank motions, both single-phase and multi-phase simulations provide similar predictions of global sloshing behavior and impact forces on the tank wall. This study clarifies the applicability of both single-phase and multi-phase SPH models, providing practical guidelines for efficient and accurate simulation of violent sloshing in marine and aeronautical engineering applications.