  We propose a novel method for the direct numerical simulation of interfacial
flows involving large density contrasts, using a Volume-of-Fluid method. We
employ the conservative formulation of the incompressible Navier-Stokes
equations for immiscible fluids in order to ensure consistency between the
discrete transport of mass and momentum in both fluids. This strategy is
implemented on a uniform 3D Cartesian grid with a staggered configuration of
primitive variables, wherein a geometrical reconstruction based mass advection
is carried out on a grid twice as fine as that for the momentum. The
implementation is in the spirit of Rudman (1998) [41], coupled with the
extension of the direction-split time integration scheme of Weymouth & Yue
(2010) [46] to that of conservative momentum transport. The resulting numerical
method ensures discrete consistency between the mass and momentum propagation,
while simultaneously enforcing conservative numerical transport to arbitrary
levels of precision in 3D. We present several quantitative comparisons with
benchmarks from existing literature in order to establish the accuracy of the
method, and henceforth demonstrate its stability and robustness in the context
of a complex turbulent interfacial flow configuration involving a falling
raindrop in air.
