A Q2Q1 integrated finite element method with the semi-implicit consistent CSF for solving incompressible two-phase flows with surface tension effect

Abstract

An integrated finite element method (FEM) is proposed to simulate incompressible two-phase flows with surface tension effects, and three different surface tension models are applied to the FEM to investigate spurious currents and temporal stability. A Q2Q1 element is adopted to solve the continuity and Navier-Stokes equations and a Q2-iso-Q1 to solve the level set equation. The integrated FEM solves pressure and velocity simultaneously in a strongly coupled manner; the level set function is reinitialized by adopting a direct approach using interfacial geometry information instead of solving a conventional hyperbolic-type equation. In addition, a consistent continuum surface force (consistent CSF) model is utilized by employing the same basis function for both surface tension and pressure variables to damp out spurious currents and to estimate the accurate pressure distribution. The model is further represented as a semi-implicit manner to improve temporal stability with an increased time step. In order to verify the accuracy and robustness of the code, the present method is applied to a few benchmark problems of the static bubble and rising bubble with large density and viscosity ratios. The Q2Q1-integrated FEM coupled with the semi-implicit consistent CSF demonstrates the significantly reduced spurious currents and improved temporal stability. The numerical results are in good qualitative and quantitative agreements with those of the existing studies.