A conservative level set method for N-phase flows with a free-energy-based surface tension model

We introduce the N-phase Conservative Level Set Free-Energy-based Surface Tension model (NCLS-FEST) for multiphase flow (N≥3). The model minimizes numerical overlaps of fluids and voids between fluids that are found in the standard Conservative Level Set (CLS) method for three fluid phases. The key differences between NCLS-FEST and CLS methods are the multiphase compression-diffusion equation to ensure conservation, an interface with constant width, a physical solution with minimal overlaps and voids between phases at each time step, and a free-energy-based surface tension model. We demonstrate that the NCLS-FEST method has accurate results for N-phase fluid flows involving complicated geometrical configurations, including triple lines in the liquid lens problem for three and four fluid phases, with accurate conservation of mass. Additionally, we show that the NCLS-FEST method can be extended to N-phase fluid-solid flow, where the solid phase is modeled by a static fluid phase.