  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.
