An efficient Numerical Simulation of Incompressible Two-Phase Flows with Surface Tension

Two-phase flows in many chemical processes and transportation of oil and gas are seen. This paper presents an efficient numerical method to simulate incompressible two-phase flow with surface tension. In the incompressible Navier-Stokes equations, if surface tension effects are taken into account, a kink in the velocity field and a jump in the pressure field may be across interface that evolve with time. In order to accurate approximations of the discontinuities, pressure and velocity fields, the combination of the projection method and the extended finite element method is studied. In order to make the suitable jump conditions, an efficient projection scheme is suggested. Unlike some works that only the velocity or pressure is enriched, the enrichment of both variables is investigated. To represent discontinuities in the discrete solution fields, the extended finite element method is applied. Numerical simulation demonstrates the effectiveness of the proposed methodology