Smooth particle approach for surface tension calculation in moving particle semi-implicit method

Abstract

We present here an algorithm to solve three-dimensional multi-phase flow problems based on the moving particle semi-implicit (MPS) method. The method is fully Lagrangian and can treat flows with large deformations of the interface such as encountered in the break-up and coalescence of drops. The mean curvature and normal vector of the interface, needed for surface tension calculation, are estimated by a blending of smooth particle hydrodynamics (SPH) and MPS differential schemes. The method is applied to two problems: the free oscillation of a droplet and the transition of a falling drop into a vortex ring. The results are consistent with theory and experiment. This method can be successfully applied to the calculation of a process in planetary core formation, where centimetre scale liquid metal droplets form an emulsion in liquid silicate.