A weakly compressible smoothed particle hydrodynamics framework for melting multiphase flow

In this study, the transient process of solid–liquid phase change is modeled and simulated by the multiphase smoothed particle hydrodynamics (SPH) method. First, to simulate the interfacial behaviors of melt liquids, the multiphase SPH model is established for immiscible viscous fluids with a large density ratio, where the environmental liquid surrounding the solid phase is considered, and the surface tension of the melt liquid can be accurately modeled by the continuum surface force method. Based on the multiphase model, the thermal dynamics model is incorporated to describe the heat conduction process. The solid–liquid phase change is realized by directly switching the state of the concerned SPH particle, where the absorbed latent heat is computed by the phase change model. Second, the model is validated by several simulation cases, including the Stefan problem, hydrostatic pressure of the evolving fluid interface, rising of two bubbles, and square droplet deformation, and the effects of numerical parameters on simulation accuracy and stability are also discussed. Third, the integrated SPH model is applied to simulate molten droplet formation and dropping processes. The results show that an initial solid–liquid interface disappears during the melting process, and new liquid–liquid interfaces gradually form and evolve under the action of surface tension, gravity, and viscosity. Phenomena such as thin-layer fluid dynamics and capillary instabilities are also reproduced, showing the effectiveness of the model for handling multiphase flow with heat conduction and phase change.