Modeling of two-phase flows at low Capillary number with VoF method

In this work, a modified version of the FSF (Filtered Surface Force) method is presented. The method was originally developed by Raeini et al. specifically for modeling low Capillary number multiphase flows, basing its structure on a well consolidated VoF (Volume of Fluid) CSF (Continuum Surface Force) solver in OpenFOAM®. The numerical method proposed in this paper is a combination of the FSF and the CICSAM scheme of Ubbink, which has been translated into a TVD framework instead of its original NVD formulation. The capability of this scheme in compressing the interface numerically lets to simplify the FSF formulation, avoiding the modification of the indicator function for the computation of the surface tension forces. Moreover, a different formulation of the filter applied to the capillary forces is presented as a simplification of the original implementation. The time step is limited by capillary forces time scale and the Courant number is chosen as a compromise between the necessity of reducing the calculation time and the numerical diffusion of the advection schemes. The methodology is validated with several test cases, showing different problems of the classical CSF method and making comparisons with theoretical solutions.