Is the motion of a single SPH particle droplet/solid physically correct?
  In recent years the Smoothed Particle Hydrodynamics (SPH) approach gained popularity in modeling multiphase and free-surface flows. In many situations, due to certain reasons, interface and free-surface fragmentation occurs. As a result single SPH particle solids/droplets of one phase can appear and travel through other phases. In this paper we investigate this issue focusing on a movement of such single SPH particles. The main questions we try to answer here are: is movement of such particles physically correct? What is its physical size? How numerical parameters affect on it? With this in mind we performed simple simulations of solid particles falling due to gravity in a fluid. Considering three different diameters of a single particle, we compared values of the drag coefficient and the velocity obtained through the SPH approach with the experimental and the analytical reference data. In the way to accurately model multiphase flows with free-surfaces we proposed and validated a novel SPH formulation. 
Kamil Szewc, Katarzyna Walczewska-Szewc, Micha{\l} Olejnik
physics.comp-ph physics.flu-dyn