Discontinuity-aware physics-informed neural network for phase-field method in three-phase flow with phase change

Abstract

Physics-informed neural networks (PINNs) have been applied to simulate multiphase flows, yet they are limited in modeling phase changes and sharp interfaces due to optimization conflicts in the strongly coupled Allen-Cahn, Cahn-Hilliard, and Navier-Stokes equations and the intrinsic smoothness bias of neural representations near discontinuities. To mitigate these limitations, this study presents a discontinuity-aware physics-informed neural network (DPINN) based on the phase-field method to resolve sharp interfaces and phase changes in multiphase flows. It incorporates a discontinuity-aware network architecture to mitigate spectral bias and automatically detect and model sharp interfacial dynamics, and a learnable local artificial viscosity term to stabilize the calculation near steep gradients. During optimization, adaptive time-marching and loss-balancing strategies are employed to reduce long-horizon errors and mitigate gradient conflicts, ensuring accurate capture of phase changes. Numerical experiments on two-phase reversed single-vortex and bubble-rising problems demonstrate that DPINN accurately resolves sharp interfacial dynamics, while conventional PINNs fail to converge. The method is further extended and tested in a three-phase droplet-icing case, where the viscosity and density ratios between ice, water, and air exceed seven and three orders of magnitude, respectively. The predicted phase change dynamics and sharp pointy-tip formation show excellent agreement with the reference, highlighting the robustness of the proposed approach.