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.

翻译：精确模拟高密度比（量级约为100,000）两相流的动力学特性对于众多材料科学与制造应用至关重要。本研究通过微重力环境下熔融金属振荡的数值模拟，分析了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关键因素。我们提出了一种基于投影的计算框架，用于求解具有大密度比的两相流的热力学一致Cahn-Hilliard Navier-Stokes方程组。该框架采用了基于Khanwale等人提出的Helmholtz-Hodge分解的压力解耦求解器改进版本（"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）。我们在多个经典问题上验证了我们的数值方法，包括毛细波和单气泡上升问题。我们还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。通过成功模拟三个具有极大密度比（10,000-100,000:1）的截然不同的物理系统，并获得了此前文献中未曾报道的结果，我们进一步证明了该框架的鲁棒性。