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

TL;DR

This paper introduces an energy-stable Smoothed Particle Hydrodynamics (SPH) discretization for the Navier-Stokes-Cahn-Hilliard model, enabling accurate simulation of incompressible two-phase flows with conservation and dissipation properties.

Contribution

It is the first to develop an energy-stable SPH discretization for the NSCH model, ensuring mass, momentum conservation, and energy dissipation in a Lagrangian framework.

Findings

The proposed SPH method conserves mass and momentum.

It inherits energy dissipation properties at the discrete level.

Numerical experiments validate the method's effectiveness.

Abstract

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