Moving Particle Semi-implicit (MPS) method is a particle method which has been developed to analyze incompressible flows with free surfaces. Fluids are represented by particles which move in fully Lagrangian description. Since grids are not necessary, complex motion of free surfaces can be calculated without grid tangling or numerical diffusion. In the MPS method, a differential equation system is transformed to particle dynamics using the models representing differential operators. Incompressibility is solved by the Poisson equation of pressure to keep the particle number density constant. Solid mechanics is also modeled by particles and fluid-structure interaction can be solved. Calculation examples are provided in this paper: collapse of a water column, melt droplet fragmentation, sloshing with tank deformation, nucleate boiling and droplet breakup. These examples show that the MPS method is a powerful tool to investigate complex behaviors of free surfaces and multiphase flows.

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