Volume tracking of interfaces having surface tension in two and three dimensions

Abstract

. Solution algorithms are presented for tracking interfaces with piecewise linear (PLIC) volume-of-fluid (VOF) methods on Eulerian grids (structured and unstructured) in two and three dimensions. We review the theory of volume tracking methods, derive appropriate volume evolution equations, identify and present solutions to the basic geometric functions needed for interface reconstruction and volume fluxing, and provide algorithm templates for modern 2-D and 3-D PLIC VOF interface tracking methods. We discuss some key issues for PLIC VOF methods, namely the method used for time integration of fluid volumes (operator splitting, unsplit, Runge-Kutta, etc.) and the estimation of interface normals. We also present our latest developments in the continuum surface force (CSF) model for surface tension, namely extension to 3-D and variable surface tension effects. We identify and focus on CSF model issues that become especially critical on fine meshes with high density ratio interfacial flows...