Fast detection of free surface and surface tension modelling via single-phase SPH

Surface tension plays a crucial role in many practical issues ranging from the bubble and droplet dynamics to the super-hydrophilic and hydrophobic bio-inspired designs. Current smoothed particle hydrodynamics models for surface tension are mostly multiphase-based and computationally expensive. In this work, we propose a single-phase model of surface tension based on fast free-surface detections. We develop two free-surface detection algorithms: (1) a two-step detection combining the number of neighboring particles method and the arc-method, and (2) a central angle-based method, which is proved to be much more efficient than the reference counterparts. The central angle method is incorporated into the single-phase model. We verify the single-phase model through several droplet dynamics simulations including initially squared droplets, the oscillating droplet, binary head-on coalescence of droplets, and the wetting problems. Compared with the multiphase solver, this single-phase model is much simpler in the algorithm, more efficient in computation, and meanwhile retains good accuracy and robustness. Although the problems studied in this work are limited to 2D cases, the single-phase model lends itself naturally to large-scale 3D scenarios. The free-surface detection algorithms can also be applied in other meshfree methods.