Robust treatment for the coarse/fine interface of adaptive mesh in the simulation of two-phase flow

We propose a numerical framework for simulating two-phase flow considering gravity and surface tension, and implement it with adaptive mesh. The framework employs a pressure compensation method and a jump model, ensuring accurate modeling of gravity and surface tension when the interface crosses between adaptive meshes of different refinement levels. Additional treatments have been developed to accommodate existing interface capturing and curvature estimation approaches for the adaptive mesh. The method is straightforward to implement and significantly reduces the unnecessary refinement around the free surface. Numerical validations demonstrate the robustness of the treatment for coarse/fine interfaces, with overall accuracy converging and comparable to results obtained with a uniform mesh. Furthermore, the numerical approach accurately reproduces the physics of bubble rising and jet capillary breakup.