Comparison between the diffuse interface and volume of fluid methods for simulating two-phase flows

Abstract

A wide variety of interface capturing methods have been introduced for simulating two-phase flows throughout the years. However, there is a noticeable dearth of literature focusing on objective comparisons between these methods, especially when they are coupled to the momentum equation and applied in physically relevant regimes. In this article, we compare two techniques for simulating two-phase flows that possess attractive qualities, but belong to the two distinct classes of diffuse interface (DI) and volume of fluid (VOF) methods. Both of these methods allow for mass-conserving schemes that can naturally capture large interfacial topology changes omnipresent in realistic two phase flows. The DI solver used in this work is based on a conservative and bounded phase field method, developed recently. Similar to level set methods, this diffuse interface method takes advantage of the smoothness of the phase field in computing curvature and surface tension forces. Geometric VOF methods track the fractional tagged volume in a cell. The specific geometric VOF scheme used here is a discretely conservative and bounded implementation that uses geometric algorithms for unsplit advection and interface reconstruction, while employing height functions for normal and curvature calculation. We present a quantitative comparison of these methods on Cartesian meshes in terms of their accuracy, convergence rate, and computational cost using canonical two-dimensional (2D) two-phase test cases: a very dense drop moving through a quiescent gas, the Rayleigh-Taylor instability, an equilibrium static drop, an oscillating drop and the damped surface wave. We further compare these methods in their ability to resolve thin films by simulating the impact of a water drop on a deep water pool. Using results of these studies, we suggest qualitative guidelines for selection of schemes for two-phase flow calculations.

Numerical investigation of the interactions between a low-hypersonic shock wave and a water droplet: VOF and DI methods comparison

“…This observation can be linked to those of [40], where Mirjalili showed that a VOF approach was more accurate than a DI approach to capture the interface position on an equivalent mesh, for several multiphase configurations. This author then showed that VOF and DI methods provide actually equivalent results when the DI mesh resolution is twice that of VOF [40]. It appears that both codes predict the bow shock to be at the same location, in spite of the differences in droplet shape.…”

“…The front droplet position seems to be better evaluated by the VOF method when T > 2, based on the comparison with the experimental data from [21]. This observation can be linked to those of [40], where Mirjalili showed that a VOF approach was more accurate than a DI approach to capture the interface position on an equivalent mesh, for several multiphase configurations. This author then showed that VOF and DI methods provide actually equivalent results when the DI mesh resolution is twice that of VOF [40].…”

MFC: An open-source high-order multi-component, multi-phase, and multi-scale compressible flow solver

“…Interface-capturing methods instead treat interfaces as discontinuities in material properties via advected volume fractions. Such methods are generally more efficient than interface-tracking schemes [36] and can achieve discrete conservation by simply solving the governing equations in conservative form. However, they also smear material interfaces via numerical diffusion [37][38][39].…”

Phase-field simulation of core-annular pipe flow

“…Furthermore, the cost of computing the curvature of the interface rises linearly with the interfacial area. Thus, in problems with large interfacial areas and deformations, such as in non-dilute turbulent dispersions, the additional computational cost of these methods is substantial [19].…”