The smoothed particle hydrodynamics method has been applied in modeling violent flows with the free surface. Much effort has been made in reducing the computational costs in simulating the three-dimensional two-phase flows with the violently deformed free surface and breaking waves. Although the adaptive particle refinement approach has been developed to concentrate fine resolution only in the region of interest, its efficiency still hardly meets the demand of large-scale numerical simulation. In order to improve its efficiency further, a multi-cell linked list algorithm coupling with the adaptive particle refinement for the smoothed particle hydrodynamics model is implemented in the graphic processing unit-based code. Particles are identified not only by its position but also by its resolution and trait. The accuracy of the numerical model for solving two-phase flows with the free surface is validated through computing a two-dimensional dam-break flow and the hydrodynamic flows of spheres vertically entering the water from the air. The numerical results agree well with the experimental data available. For the cases of water entry of a sphere of different densities, the development of open cavity and cavity sealing is discussed in terms of the pinch-off depth and the corresponding sphere depth. Simulations show that the smoothed particle hydrodynamics method with the adaptive particle refinement possesses the characteristics of good accuracy, time-saving, and high efficiency in simulating three-dimensional two-phase flows.
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