Accurately modeling the dynamics of high-density ratio ($\mathcal{O}(10^5)$) two-phase flows is important for many applications in material science and manufacturing. In this work, we consider numerical simulations of molten metal undergoing microgravity oscillations. Accurate simulation of the oscillation dynamics allows us to characterize the interplay between the two fluids' surface tension and density ratio, which is an important consideration 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 under these large density ratios. A modified version of the pressure-decoupled solver based on the Helmholtz-Hodge decomposition presented in Khanwale et al. [$\textit{A fully-coupled framework for solving Cahn-Hilliard Navier-Stokes equations: Second-order, energy-stable numerical methods on adaptive octree based meshes.}$, Journal of Computational Physics 475 (2023): 111874] is used. We present a comprehensive convergence study to investigate the effect of mesh resolution, time-step, and interfacial thickness on droplet-shape oscillations. We deploy our framework to predict the oscillation behavior of three physical systems exhibiting very large density ratios ($10^4-10^5:1$) that have previously never been performed.

翻译：精确模拟高密度比（$\mathcal{O}(10^5)$）两相流的动力学行为对于材料科学与制造领域的许多应用至关重要。在本工作中，我们研究了经历微重力振荡的熔融金属的数值模拟。对振荡动力学的精确模拟使我们能够表征两种流体表面张力与密度比之间的相互作用，这是地面制造应用中的一个重要考量因素。我们提出了一种基于投影的计算框架，用于求解在此类大密度比条件下两相流的热力学一致Cahn-Hilliard Navier-Stokes方程组。该框架采用了基于Helmholtz-Hodge分解的压力解耦求解器的一个改进版本，该求解器源自Khanwale等人[$\textit{A fully-coupled framework for solving Cahn-Hilliard Navier-Stokes equations: Second-order, energy-stable numerical methods on adaptive octree based meshes.}$, Journal of Computational Physics 475 (2023): 111874]的工作。我们进行了全面的收敛性研究，以探讨网格分辨率、时间步长和界面厚度对液滴形状振荡的影响。我们应用该框架预测了三个物理系统的振荡行为，这些系统表现出此前从未模拟过的极大密度比（$10^4-10^5:1$）。