Stable multiphase moving particle semi-implicit method for incompressible interfacial flow

The moving particle semi-implicit (MPS) method is extended into a multiphase MPS (MMPS) method, where multiphase fluids are modeled as a multi-viscosity and multi-density fluid. Interparticle viscosity and density are adopted to model the interaction between particles of different phases. However, such a straightforward extension is prone to instability because the light particles at the interface suffer from exceptionally high acceleration. Therefore, two approaches, MMPS-HD (harmonic density) and MMPS-CA (continuous acceleration), are proposed to suppress the instability. In the first approach, harmonic mean interparticle density is applied to discretize the multiphase pressure Poisson equation to avoid the exceptionally high acceleration at the interface. In the second approach, new MMPS formulations are derived from the locally weighted average of interaction acceleration between particles to guarantee the continuity of acceleration and velocity. The particle stabilizing term (PST) is then decoupled from the original pressure gradient model and adopts the single-phase formulation to guarantee stability. The developed multi-viscosity and -density models are verified using the multi-fluid Poiseuille flow and Rayleigh–Taylor instability, respectively. Furthermore, two benchmark cases of rising bubbles in 2D and 3D with a wide range of density and viscosity ratios are simulated to demonstrate the capability and robustness of the proposed methods in complex multiphase flows. The proposed method can produce stable and reliable results up to a high density ratio of approximately 1000 and viscosity ratio of approximately 100.