High fidelity anisotropic adaptive variational multiscale method for multiphase flows with surface tension

We propose in this work an adaptive variational multiscale method for two-fluid flows with surface tension. A level set function is used to provide a precise position of the interfaces. The implementation of the surface tension in the context of the Continuum Surface Force is proposed to circumvent the capillary time step restriction. The obtained system is then solved using a new derived Variational Multiscale stabilized finite element method designed to handle the abrupt changes at the interface and large density and viscosity ratios. Combined with an a posteriori error estimator, we show that anisotropic mesh adaptation provides highly stretched elements at the interfaces and thus yield an accurate modeling framework for two-phase incompressible isothermal flows. Stable and accurate results are obtained for all two- and three-dimensional numerical examples. To the best of our knowledge, these are the first simulation results for representative time-dependent three-dimensional two-fluid flow problems using an implicit treatment of the surface tension and a dynamic unstructured anisotropic mesh adaptation.