Application of semi-segregated finite element method to two-phase problems with a surface tension effect

A semi-segregated finite element method (FEM) is introduced for solving two-phase flows with a surface tension effect. The FEM code is spatially discretized with a Q2Q1 element using quadratic and linear shape functions for velocity and pressure, respectively. For temporal discretization, coupled Crank Nicholson and third-order Runge Kutta methods are employed. Furthermore, a consistent continuum surface force (CSF) model is used with the same basis function for pressure and surface tension terms. Next, a static bubble and two rising bubble problems are investigated for validation. In the static bubble, the consistent CSF model performs well when estimating pressure distribution, but it creates larger spurious currents than the existing integrated FEM. For the case of rising bubbles, the semi-segregated FEM provides consistent results with the integrated FEM, and its computational cost is less expensive except for the case of viscous force-dominated flows with dense grids.