Modeling of two-phase flows with surface tension by finite pointset method (FPM)

A meshfree method for two-phase immiscible incompressible flows including surface tension is presented. The continuum surface force (CSF) model is used to include the surface tension force. The incompressible Navier–Stokes equation is considered as the mathematical model. Application of implicit projection method results in linear second-order partial differential equations for velocities and pressure. These equations are then solved by the finite pointset method (FPM), which is a meshfree and Lagrangian method. The fluid is represented as finite number of particles and the immiscible fluids are distinguished by the color of each particle. The interface is tracked automatically by advecting the color functions for each particle. Two test cases, Laplaceʹs law and the Rayleigh–Taylor instability in 2D have been presented. The results are found to be consistent with the theoretical results.