Development of Interphase Particle for multiphase flow simulation by ISPH

In conventional incompressible smoothed particle hydrodynamics (ISPH), volume conservation is ensured by maintaining a constant particle number density at each particle. However, in multiphase flow simulations, the presence of different densities can disrupt the compatibility with the continuity equation based on the particle number density. This often leads to numerical instabilities and inaccuracies at the interface. To address this issue, this study proposes a novel, stable multiphase scheme introducing a mathematical construct termed the Interphase Particle (IP). The IP acts as an agent that mediates interparticle forces between different phases. Unlike conventional interpolation-based or over-grid methods, the IP is integrated directly into the Pressure Poisson Equation matrix, allowing the pressure for all phases to be solved simultaneously within a single discretization space. The good performance of the proposed scheme in the energy conservation and reproducibility of interfaces including wall boundaries and numerical stability was validated through several benchmark tests: two-phase hydrostatic fluid columns, an oscillating droplet, the merging of rising bubbles, and a dam break. • A stable multiphase scheme is newly proposed for projection particle methods. • The new scheme is referred to as the Interphase Particle (IP). • IP is introduced to mediate multi-phase forces as a virtual particle. • IP is integrated into the Pressure Poisson Equation and provides mass-volume-density consistent pressure fields without conventional over-grid interpolation. • IP enables accurate and stable simulations of multiphase flows with high density ratios.