Recent Progress on Mesh-free Particle Methods for Simulations of Multi-phase Flows: A Review

The discrete element method (DEM) and the moving particle semi-implicit (MPS) method are the most popular mesh-free particle methods in the discontinuum and continuum. This paper describes a state-of-the-art modeling on multi-phase flows using these mesh-free particle methods. Herein, a combinational model of the signed distance function (SDF) and immersed boundary method (IBM) is introduced for an arbitrary-shaped wall boundary in the DEM simulation. Practically, this model uses a simple operation to create the wall boundary. Although the SDF is a scalar field for the wall boundary of the DEM, it is useful for the wall boundary of the CFD through combination with the IBM. Validation tests are carried out to demonstrate the adequacy of the SDF/IBM wall boundary model. Regarding the mesh-free particle method for continuum, the phase change problem is one of the challenging topics, as the solid state is usually modeled by extremely high viscous fluid in the phase change simulation. The phase change simulation is shown to be efficiently performed through an implicit algorithm and a heat flux model in the MPS method. The adequacy of these models is verified by the numerical examples.