A Momentum-Conserving Weakly Compressible Navier–Stokes Solver for Simulation of Violent Two-Phase Flows with High Density Ratio

A consistent and conservative formulation for mass and momentum transport is proposed in the context of simulating incompressible two-phase flows by using weakly compressible method. Combined with the evolving pressure projection method to prevent oscillation of the solution induced by the acoustic wave, this solver aims at a robust and accurate computation of violent two-phase flows with a high density ratio, while taking advantage of fully explicit time integration of the weakly compressible Navier–Stokes equations. Coupled with the volume of fluid method for capturing interfaces, the mass and momentum fluxes are evaluated in a consistent manner using the finite volume method. In addition, a special implementation of the pressure projection is devised to avoid velocity-pressure decoupling on a collocated grid. The solver's accuracy and stability are demonstrated through various two-phase flow simulations, including dam break and liquid jet atomization scenarios, emphasizing its momentum-conserving properties.