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The weakly compressible SPH (WCSPH) method is known suffering from low computational efficiency, or unnatural voids and unrealistic phase separation when it is applied to simulate highly violent multi-phase flows with high density ratio, such as that between water and air. In this paper, to remedy these issues, we propose a multi-phase WCSPH method based on a low-dissipation Riemann solver and the transport-velocity formulation. The two-phase Riemann problem is first constructed to handle the pairwise interaction between fluid particles, then modified for the fluid-wall interaction to impose the solid wall boundary condition. Since the method uses the same artificial speed of sound for both heavy and light phases, the computational efficiency increases greatly. Furthermore, due to the transport-velocity formulation employed for the light phase and application of the two-phase Riemann problem, the unnatural voids and unrealistic phase separation are effectively eliminated. The method is validated with several 2-and 3D cases involving violent water-air flows. The results have been compared with existing experimental data, previous numerical and analytical solutions, where the proposed method demonstrates good robustness, improved or comparable accuracy, respectively, comparing to previous methods with same choice of sound speed or those with much less computational efficiency.

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Implementing particle-interaction configuration and time integration are performance intensive essentials of particle-based methods. In this paper, a dualcriteria time-stepping method is proposed to improve the computational efficiency of the weakly-compressible smoothed particle hydrodynamic (WCSPH) method for modeling incompressible flows. The key idea is to introduce an advection time criterion, which is based on fluid velocity field, for recreating the particle-interaction configuration. Within this time criterion, several steps of pressure relaxation determined by the acoustic time criterion, based on the artificial speed of sound, can be carried out without updating the particle interaction configuration and much larger time-step sizes compared with the conventional counterpart. The method has shown optimized computational performance through CPU cost analysis. Good accuracy and performance is obtained for the presented benchmarks implying promising potential of the proposed method for incompressible flow and fluid-structure interaction simulations.

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