A multi-resolution two-phase smoothed particle hydrodynamics method for modeling breaking bow waves

Abstract

When a ship sails at high speed, breaking bow waves are formed at the bow, resulting in the component of ship resistance associated with wave-breaking-induced energy dissipation and air entrainment. In this paper, we propose a multi-resolution multi-graphics processing unit two-phase smoothed particle hydrodynamics (SPH) method to simulate the breaking bow waves of a KRISO Container Ship (KCS) model at different Froude numbers. Simulations of five different Froude numbers (Fr = 0.377, 0.400, 0.424, 0.450, 0.470) are carried out. The total number of particles reaches 1.1×10⁸. The computed wave elevations are compared with the experimental results, which were obtained with the KCS model in a circulating water channel using a binocular stereo reconstruction method. A good agreement is found. The mean wave elevation and its standard deviation, the velocity field, and the vortex structures are analyzed. The results show that increasing the Froude number can lead to more intense fluctuations in wave elevation. The breaking bow waves at the first two Froude numbers are classified as spilling breakers, while those at the last three Froude numbers are plunging breakers. The area of the cavity formed at the impact cross-section increases with the increase of the Froude number. Three main vortex structures are identified for plunging breakers. Vorticity is distributed at the wave crest for spilling breakers, while for plunging breakers, a significant amount of vorticity is found around the cavity.