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We propose a novel method for the direct numerical simulation of interfacialflows involving large density contrasts, using a Volume-of-Fluid method. Weemploy the conservative formulation of the incompressible Navier-Stokesequations for immiscible fluids in order to ensure consistency between thediscrete transport of mass and momentum in both fluids. This strategy isimplemented on a uniform 3D Cartesian grid with a staggered configuration ofprimitive variables, wherein a geometrical reconstruction based mass advectionis carried out on a grid twice as fine as that for the momentum. Theimplementation is in the spirit of Rudman (1998) [41], coupled with theextension of the direction-split time integration scheme of Weymouth & Yue(2010) [46] to that of conservative momentum transport. The resulting numericalmethod ensures discrete consistency between the mass and momentum propagation,while simultaneously enforcing conservative numerical transport to arbitrarylevels of precision in 3D. We present several quantitative comparisons withbenchmarks from existing literature in order to establish the accuracy of themethod, and henceforth demonstrate its stability and robustness in the contextof a complex turbulent interfacial flow configuration involving a fallingraindrop in air.

A novel momentum-conserving, mass-momentum consistent method for interfacial flows involving large density contrasts