A comparison of interface tracking methods in a low-Mach formulation

Abstract

The objective of the present work is to compare the main Eulerian sharp-interface tracking methods using up-to-date numerical strategies from the literature. The study is focused on the specific case of low-Mach number formulation for the phase dynamics, and on a finite-volume cartesian-grid discretization. Volume of fluid and Level Set methods both rely on the resolution of an Eulerian transport equation that describes the interface and an additional step to prevent huge deviation from the interface representation due to numerical diffusion and dispersion in the transport step. In the VOF framework, this results in the transport of the volume fraction with a piecewise linear construction of the interface (PLIC). In the LS framework, this takes the form of a distance function transport which can be either a signed distance (here called Standard Level Set (SLS)) or an hyperbolic tangent (called the Conservative Level Set (CLS)) followed by a reinitialization step which ensures that the transported variable remains a signed distance or an hyperbolic tangent respectively. For each method, the numerical scheme used for advection and additional step are selected because of their proven accuracy and effectiveness in the literature for our specific framework. Our comparison is based on 2D and 3D canonical cases of the literature (Zalesak’s Disk rotation, vortex-in-a-box, sphere deformation). Our attention is drawn on a detailed analysis of mass conservation and transport accuracy, with the use of shared metrics for all methods.