Surface tension simulations with corrected ALE-ISPH and density-based shifting technique

This work shows the extension of a corrected Arbitrary Lagrangian Eulerian Incompressible Smoothed Particle Hydrodynamics (ALE-ISPH) method to surface tension simulations. In this context, the term “corrected” refers to the fact that all derivative operators are modified to enable first-order accuracy. Moreover, particles move according to a transport velocity, which is the summation of the material velocity and a small shifting of particle location to promote a smooth particle distribution at every step; hence, it is based on an ALE formulation. Using this method as a basis, we propose some small empirical modifications to the conventional curvature-based calculation of surface tension forces to simulate this phenomenon. Furthermore, we propose a special wall boundary treatment including ghost particles to reproduce the desired contact angles. Validation and verification tests include the obtaining of the theoretical Laplace pressure in a water droplet, the analysis of the frequency of an oscillating 3D droplet, the comparison of the capillary rise with the theoretical value and the collision of water droplets compared to physical experiments. All numerical simulations were successful, so we consider this to be a reasonable method to simulate the phenomena of surface tension under a wide range of conditions.