A Material Interface Transition Algorithm for Multiphase Flow

Volume tracking method, also referred to as the volume-of-fluid (VOF) method introduces “numerical surface tension” that breaks a filament into a series of droplets whenever the filament is under-resolved. Adaptive mesh refinement can help avoid under-resolution, but a fully-developed flow will still generate filaments that cannot be resolved without enormous computational cost. We propose a complementary new approach that consists of transitioning to a continuous interface representation (i.e. without interface reconstruction) in regions of under-resolved interfacial curvature where volume tracking has become erroneous. The price of the continuous interface treatment is a small amount of numerical mass diffusion, even if the physical interface is immiscible. However, we have found that for certain measures, the overall accuracy is greatly improved by using our transitioning algorithm. The algorithm is developed in the context of the single fluid formulation of the incompressible Navier-Stokes equations. Numerical standard vortices advection test cases and Rayleigh-Taylor instability computations are presented to illustrate the transition algorithm potential.