A new efficient momentum preserving Level-Set/VOF method for high density and momentum ratio incompressible two-phase flows

Many two-phase flows relevant to natural and industrial applications are characterized by high density ratios and high shears at the interface. These peculiarities make numerical simulations of such kind of flows still challenging. In particular, incompressible Level-Set/Volume-of-Fluid-based solvers are affected by the onset of diverging spurious velocities close to the interface. In this paper a new strategy, able to overcome these numerical instabilities, is described for staggered Cartesian grids. In order to achieve a consistent mass-momentum advection, a new auxiliary continuity equation is introduced and resolved along the momentum equations in the velocity control volumes. The mass fluxes are evaluated through the Volume-of-Fluid color function and directly used to calculate the momentum convective term. Several high-density test cases (the density ratio going from 103 to 106) are presented: the new algorithm shows significant improvements in stability and accuracy over the standard velocity based advection methods, together with a very low increase in computational time, estimated at 5%÷10%. Therefore, it is suitable to simulate more complex and realistic high density ratio two-phase flows, such as the breakup of a liquid jet in cross-flow here described.