A Q2Q1 finite element/level-set method for simulating two-phase flows with surface tension

A Q2Q1 (quadratic velocity/linear pressure) finite element/level-set method was proposed for simulating incompressible two-phase flows with surface tension. The Navier-Stokes equations were solved using the Q2Q1 integrated FEM, and the level-set variable was linearly interpolated using a 'pseudo' Q2Q1 finite element when calculating the density and viscosity of a fluid to avoid an unbounded density/viscosity. The advection of the level-set function was calculated through the Taylor-Galerkin method, and the direct approach method is employed for reinitialization. The proposed method was tested by solving several benchmark problems including rising bubbles exhibiting a large density difference and the surface tension effect. The numerical results of the rising bubbles were compared with the existing results to validate the benchmark quantities such as the centroid, circularity, and rising velocity. Furthermore, we focused our attention mainly on mass conservation and time-step. We observed that the present method represented a convergence rate between 1.0 and 1.5 orders in terms of mass conservation and provided more stable solutions even when using a larger time-step than the critical time-step that was imposed because of the explicit treatment of surface tension.