A diffuse-interface model for smoothed particle hydrodynamics

TL;DR

This paper introduces a novel smoothed particle hydrodynamics (SPH) model based on diffuse-interface theory for simulating two-phase fluids with dynamic interfaces, eliminating the need for explicit interface tracking.

Contribution

The paper develops a diffuse-interface SPH model that captures interface dynamics without explicit surface detection, incorporating surface tension and finite interface thickness.

Findings

Model successfully simulates two-phase fluid behavior.

No explicit interface tracking or curvature computation needed.

Validated through 1D and 2D SPH simulations.

Abstract

Diffuse-interface theory provides a foundation for the modeling and simulation of microstructure evolution in a very wide range of materials, and for the tracking/capturing of dynamic interfaces between different materials on larger scales. Smoothed particle hydrodynamics (SPH) is also widely used to simulate fluids and solids that are subjected to large deformations and have complex dynamic boundaries and/or interfaces, but no explicit interface tracking/capturing is required, even when topological changes such as fragmentation and coalescence occur, because of its Lagrangian particle nature. Here we developed an SPH model for single-component two-phase fluids that is based on diffuse-interface theory. In the model, the interface has a finite thickness and a surface tension that depend on the coefficient, k, of the gradient contribution to the Helmholtz free energy functional and the density dependent homogeneous free energy. In this model, there is no need to locate the surface (or interface) or to compute the curvature at and near the interface. One- and two-dimensional SPH simulations were used to validate the model.