Comparative analysis of volume of fluid and phase–field methods for numerical simulations of two-phase flows

Abstract

A comprehensive study is conducted to analyze various methods for capturing the fluid interface in numerical simulations of two-phase flows. The primary objective is to compare the performance of volume of fluid (VOF) methods, based on a sharp interface description, and phase-field (PF) methods, where diffuse transition layers are used instead. To this end, a series of numerical simulations is conducted by using an in-house solver with four different interface-capturing methods: an algebraic TVD-VOF (AVOF), a geometric PLIC-VOF (GVOF), and two PF methods, based respectively on the conservative Allen–Cahn (CAC) and profile-corrected Cahn–Hilliard (CCH) formulations. These simulations aim to reproduce commonly used benchmark test cases as well as more complex practical applications, such as oceanic wave breaking and the sloshing phenomena of fluids within containers. The results highlighted the strengths and weaknesses of each method under various conditions, offering insights into their accuracy and computational costs. Among the methods, the GVOF approach consistently demonstrated higher accuracy in predicting the interface geometry, along with superior grid convergence properties, making it a reliable choice for a wide range of numerical simulations. The AVOF method offers a reliable alternative, delivering accurate results but facing some challenges in capturing smaller fluid structures and showing performance degradation in highly nonlinear scenarios. The PF methods are less accurate in predicting interface geometry, but perform better in terms of surface tension accuracy, yielding reduced spurious currents. The CAC method proves computationally efficient and simple to implement but faces time step limitations that necessitate future improvement for high-fidelity simulations. Finally, the CCH method performs least accurately across test conditions and it also incurs the highest computational cost among the methods tested. These outcomes may provide valuable insights for researchers in selecting the most suitable numerical method for their specific applications.