Accurate calculation of the surface tension force and the droplet simulation using a particle method with moving surface mesh

Abstract

In this paper, we proposed a new particle method for numerical simulation of droplet dynamics. In the proposed method, the moving surface mesh is used to define interface between gas and liquid. The volume enclosed by the mesh represents the liquid droplet, and the outer domain is inactive gas with constant pressure. The incompressible liquid flow is calculated using a particle method, in which spatial derivatives are evaluated using an arbitrary high order accurate scheme. On the free surface, the surface stress balance equations, including surface tension and viscous stress, are adopted for the boundary conditions. Deformation of the gas-liquid interface is explicitly calculated by surface nodes that move in a Lagrangian fashion. Surface tension force is directly evaluated with high accuracy on each node utilizing the mesh shape. As numerical verification, simulations of three benchmark problems, namely circular patch test, Laplace pressure test and 2D droplet (liquid column) oscillation problems with different oscillation modes, have been carried out. The computation results were compared with the theoretical solutions, and excellent agreements were obtained. As a result, high accuracy and validity of the proposed computational method were confirmed.