A new SPH density formulation for 3D free-surface flows

In this paper, a new density formulation for free surface simulations using SPH is presented. This new approach is applicable to surface-tension driven free surface flows with strong topological changes. The density is corrected for each particle by analytically calculating the missing volume of the support domain. This calculation depends on two parameters: the local curvature and the distance of each particle to the free surface. This method was validated and compared with the density evolution method for two test cases: the square droplet and the Rayleigh-Plateau instability. It shows more stable results and a better representation of the free surface.