A Consistent Mass-Momentum Advection Method for the Simulation of Large-Density-ratio Two-Phase Flows

In present study, a simple and robust method is proposed to calculate the mass and momentum flux in the simulation of large-density-ratio interfacial flows. An auxiliary continuity equation is introduced and solved in a consistent manner with the momentum equations. This method ensures the consistency of the mass and mo-mentum transportation in both phases. The erroneous interfacial momentum transfer often arising in traditional two-phase flow simulations can be suppressed. Moreover, this method can be extended straightforwardly to work with any of the VOF (Volume of Fluid) -type interface capturing methods. Present algorithm is implemented on an in-house code with block-structured adaptive mesh refinement (BAMR) (Liu and Hu, 2018) technologies, and is highly applicable for the massively parallel computations. We demonstrate the numerical stability and ac-curacy through a series of typical two-phase flow tests with high density ratios. Finally, the simulation of at-omization of liquid sheet is considered to further demonstrate the capability in simulating surface tension driven flows. Numerical results show the spurious air velocity and unphysical interface fragmentation are completely avoided. Present consistent method exhibits much better performance in suppressing the excessive kinetic energy introduced by the two-phases co-existing cells. Moreover, the method is simple for implementation and is robust for the violent two-phase flow problems, even with strong shear velocity around the interface.