MPS mesh-free particle method for multiphase flows

By treating the multiphase system as a multi-density multi-viscosity fluid, a straightforward model has been proposed in this paper based on the Moving Particle Semi-implicit (MPS) mesh-free particle method for incompressible multiphase flow. The weakly-compressible MPS (WC-MPS) formulation (developed by the authors) is used to solve a single set of equations for all of the phases. In the model, the multiphase forces are introduced in a straightforward way. Dealing with multi-viscosity systems, different methods for defining the viscosity, by which particles of different phases interact, is examined. To evaluate the accuracy of each of these methods, a stratified multi-viscosity Poiseuille flow test case is used and model results are compared with the analytical solution. The results show that selection of this interaction viscosity has an important role in the accuracy of the results. The model is then validated and applied to two basic hydrodynamic instability cases (Rayleigh–Taylor and Kelvin–Helmholtz instabilities). The results are then compared to a mesh-based model (with volume of fluid interface tracing method) to examine the ability of the model to deal with the multi-density systems. Comparisons show the model has reasonable accuracy. The results of this work offer the potential of modeling of multiphase incompressible immiscible systems in an extensive range of conditions using MPS.