An energy-stable Smoothed Particle Hydrodynamics discretization of the Navier-Stokes-Cahn-Hilliard model for incompressible two-phase flows

Varieties of energy-stable numerical methods have been developed for incompressible two-phase flows based on the Navier-Stokes–Cahn–Hilliard (NSCH) model in Eulerian framework, while few investigations made Lagrangian framework. Smoothed particle hydrodynamics (SPH) is a popular mesh-free method solving complex fluid flows. In this paper, we present pioneering study SPH discretization NSCH We prove that inherits mass and momentum conservation energy dissipation properties at fully discrete level. With projection procedure to decouple continuity equations, scheme meets divergence-free condition. Some experiments are carried out show performance proposed model. The inheritance verified numerically.