Operator learning methods for modeling interfacial dynamics of rising bubble

Two-phase flow involves the simultaneous dynamics of two distinct phases, with numerous important implications in the industrial field. However, accurately modeling these flows, whether through experiments or numerical simulations, requires substantial computational resources to capture the complex interfacial dynamics. In this study, we tested three different neural operators—the Fourier neural operator (FNO), physics-aware recurrent convolutions (PARC), and the deep operator network (DeepONet), with the aim of accelerating the simulation of dynamics in two-phase flows. We employed two benchmark problems of single bubble rising (140 cases) to bubble condensation (50 cases) for predicting the volume fraction, pressure, velocity fields, and more. Our framework considers only initial and boundary conditions to predict the entire temporal evolution, where physical parameters such as fluid density, fluid dynamic viscosity, and surface tension coefficient are set to the initial conditions. As a result, in the single bubble rising case, FNO achieved the best accuracy, yielding a root mean square error (RMSE) of 0.0154 in predicting the volume fraction field. On the other hand, for the bubble condensation case, DeepONet exhibited the lowest RMSE value of 0.0123. Additionally, we examined the computational efficiency and distinctive characteristics of each technique, as well as its applicability to modeling two-phase flows. Overall, this study offered practical insights into utilizing neural operators for solving fundamental benchmark problems, further demonstrating the potential of neural operators as efficient surrogate models for a wide range of physical phenomena at significantly reduced computational costs.