The unstructured geometrical VOF method for industrial two-phase flows simulations with high density ratios

Incompressible two-phase flows that involve fluids with very different densities (high density ratios) are ubiquitous in natural and technical processes, and the one-field formulation of Navier-Stokes Equations (one-field NSE) is widely used to model such flows. The integral form of the one-field NSE is especially amenable for deriving and understanding the consistency between volume and mass conservation, required for incompressible two-phase flows. The phase indicator function further uniquely defines the mass flux, that must be consistently used in the mass conservation and the momentum conservation equation. These exact consistency requirements, derived from the integral form of the one-field NSE, are independent of the method used to model the fluid interface. Research into two-phase flow simulation methods for handling high density ratios is highly active; however, focusing primarily on the discrete level. In this work, we derive exact consistency requirements at the level of the mathematical model. These conditions must be tailored to the PDE discretization and fluid interface tracking methods, but they must be upheld. Since we develop numerical methods for simulating geometrically complex engineering multiphase flow systems, we discretize the one-field NSE with the consistency requirements using the unstructured Finite Volume method and validate and verify them for the unstructured Level Set / Front Tracking [1] method and plicRDF-isoAdvector, a flux-based geometrical Volume-of-Fluid method [2].