Modeling and simulations of high-density two-phase flows using projection-based Cahn-Hilliard Navier-Stokes equations

Accurately modeling the dynamics of high-density ratio (on the order of 100,000) two-phase flows is important for many material science and manufacturing applications. This work considers numerical simulations of molten metal oscillations in microgravity to analyze the interplay between surface tension and density ratio, a critical factor for terrestrial manufacturing applications. We present a projection-based computational framework for solving a thermodynamically-consistent Cahn-Hilliard Navier-Stokes equations for two-phase flows with large density ratios. The framework employs a modified version of the pressure-decoupled solver based on the Helmholtz-Hodge decomposition presented in Khanwale et al. ("A projection-based, semi-implicit time-stepping approach for the Cahn-Hilliard Navier-Stokes equations on adaptive octree meshes," Journal of Computational Physics 475 (2023): 111874). We validate our numerical method on several canonical problems, including the capillary wave and single bubble rise problems. We also present a comprehensive convergence study to investigate the effect of mesh resolution, time-step, and interfacial thickness on droplet-shape oscillations. We further demonstrate the robustness of our framework by successfully simulating three distinct physical systems with extremely large density ratios (10,000-100,000:1), achieving results that have not been previously reported in the literature.