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We develop a consistent adaptive framework in a multilevel collocated grid layout for simulating two-phase flows with adaptive mesh refinement (AMR). The conservative mo-mentum equations and the mass equation are solved in the present consistent framework. This consistent mass and momentum transport treatment greatly improves the accuracy and robustness for simulating two-phase flows with a high density ratio and high Reynolds number. The interface capturing level set method is coupled with the conservative form of the Navier–Stokes equations, and the multilevel reinitialization technique is applied for mass conservation. This adaptive framework allows us to advance all variables level by level using either the subcycling or the non-subcycling method to decouple the data ad-vancement on each level. The accuracy and robustness of the framework are validated by a variety of canonical two-phase flow problems. We demonstrate that the consistent scheme results in a numerically stable solution in flows with high density ratios(up to 106) and high Reynolds numbers(up to 106), while the inconsistent scheme exhibits non-physical fluid behaviors in these tests. Furthermore, it is shown that the subcycling and non-subcycling methods provide consistent results and that both of them can accurately resolve the interfaces of the two-phase flows with surface tension effects. Finally, a 3D breaking wave problem is simulated to show the efficiency and significant speedup of the proposed framework using AMR. 

We develop a consistent adaptive framework in a multilevel collocated grid layout for simulating two-phase flows with adaptive mesh refinement (AMR). The conservative mo-mentum equations and the mass equation are solved in the present consistent framework. This consistent mass and momentum transport treatment greatly improves the accuracy and robustness for simulating two-phase flows with a high density ratio and high Reynolds number. The interface capturing level set method is coupled with the conservative form of the Navier–Stokes equations, and the multilevel reinitialization technique is applied for mass conservation. This adaptive framework allows us to advance all variables level by level using either the subcycling or the non-subcycling method to decouple the data ad-vancement on each level. The accuracy and robustness of the framework are validated by a variety of canonical two-phase flow problems. We demonstrate that the consistent scheme results in a numerically stable solution in flows with high density ratios(up to 106) and high Reynolds numbers(up to 106), while the inconsistent scheme exhibits non-physical fluid behaviors in these tests. Furthermore, it is shown that the subcycling and non-subcycling methods provide consistent results and that both of them can accurately resolve the interfaces of the two-phase flows with surface tension effects. Finally, a 3D breaking wave problem is simulated to show the efficiency and significant speedup of the proposed framework using AMR.