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The standard weakly compressible Smoothed Particle Hydrodynamics (WCSPH) is successfully applied to multi-phase problems involving fluids with similar densities, but when density ratio increases at some order of magnitude, serious instability phenomena occur at the interface. Several remedies have been proposed based on numerical correctives that deviate from standard formulation, increasing the algorithm complexity and, sometimes, the computational cost. In this study, the standard SPH has been adapted to treat free-surface multi-phase flows with a large density ratio through a modified form of the governing equations which is based on the specific volume (i.e. the inverse of particle volume) instead of density: the former is continuous across the fluid interface while the latter is not and generates numerical instability. Interface sharpness is assured without cohesion forces; kernel truncation at the interface is avoided. The model, relatively simple to implement, is tested by simulating two-phase dam breaking for two configurations: kinematic and dynamic features are compared with reference data showing good agreement despite the reduced computational effort.

The smoothed particle hydrodynamics (SPH) method has been proved as a powerful algorithm for fluid mechanics, especially in the simulation of free surface flows with high speeds or drastic impacts. The solid boundary treatment method is important for the accuracy and stability of the numerical results, as the support domain of fluid particles is truncated near the vicinity of the boundary. This paper presents two commonly used methods for simulating a solid boundary in SPH simulations. Emphasis is placed on the description of the methods, definition of the boundary particles’ parameters, and discussion of their advantages and shortcomings. The classical dam break simulation is conducted using self-developed code and open source models such as DualSPHysics and PySPH in order to investigate the effects of the boundary methods. The results show that methods based on dynamic boundary particles can simulate the free water surface well with a good agreement with experimental results. The conclusions can also be used in research for boundary implementation methods for practical ocean and coastal engineering problems with free surface flows.

Wave breaking over a submerged step with a steep front slope and a wide horizontal platform is studied by smoothed particle hydrodynamic (SPH) method. By adding a momentum source term and a velocity attenuation term into the governing equation, a nonreflective wave maker system is introduced in the numerical model. A suitable circuit channel is specifically designed for the present SPH model to avoid the nonphysical rise of the mean water level on the horizontal platform of the submerged step. The predicted free surface elevations and the spatial distributions of wave height and wave setup over the submerged step are validated using the corresponding experimental data. In addition, the vertical distributions of wave-induced current over the submerged step are also investigated at both low and high tides.

The wave impact on marine structures is concerning in ocean and coastal engineering. Cylinders are important components of various marine structures such as piers of sea-crossing bridge, columns of oil and gas platforms and subsea pipelines. In this study, the interaction of solitary wave with a submerged horizontal cylinder and a surface-piercing vertical cylinder are numerically studied by the Smoothed Particle Hydrodynamics (SPH) code SPHinXsys. SPHinXsys is an open-source multi-physics library based on the weakly compressible SPH and invokes the low-dissipation Riemann solver for alleviating numerical noises in the simulation of fluid dynamics. The capability of SPHinXsys in reproducing the fluid fields of solitary wave propagating through cylinders is demonstrated by comparing with the experimental data. With the validation in hand, the features of the wave–structure process are examined.