Phase-field physics-informed neural networks for multiphase flow simulations in axisymmetric coordinates with applications of bubble rising in multiple regimes

While physics-informed neural networks are becoming a promising approach for multiphase flow simulations, the transition from two-dimensional to three-dimensional applications is primarily hindered by computational inefficiency. This study presents a phase-field Physics-Informed Neural Networks (PF-PINNs) specifically designed for axisymmetric multiphase flow dynamics. Adaptive time marching strategy and axisymmetric weighted sampling strategy are introduced to ensure training convergence. The framework is validated through bubble rising simulations in infinite fluid domain. Results show that the shape of the interface coincides well with numerical validation. Dynamic behaviors, including centroid trajectories, rising velocity and velocity fields are precisely captured. We also evaluate the applicable range of this method with cases over different Reynolds numbers and Bond numbers. The prediction succeeds in Re=[10, 200] and Bo=[10, 200], which demonstrates the generality of PF-PINNs in axisymmetric coordinate and the ability to capture different bubble dynamics in different regimes.