Data-Free physics-informed neural networks for modeling compressible multiphase flows

Physics-informed neural networks (PINNs), which formulate loss functions based on the residuals of governing equations, have gained increasing attention for modeling fluid mechanics. However, in compressible flows, the differential form of hyperbolic conservation laws breaks down near discontinuities due to the absence of derivatives. This limitation presents a significant challenge for data-free PINN frameworks. The challenge is further intensified in multiphase flows, where contact discontinuities exhibit more complex structures and interactions, and relevant studies remain limited. To address these challenges, this study proposes a multiphase PINN model incorporating an encoder-decoder convolutional long short-term memory (ConvLSTM) deep learning framework to enable deep feature extraction and global residual computation. A multiphase Godunov-type finite volume method (FVM) loss function is developed based on a highly robust five-equation model. By employing a Godunov-type discretization derived from the weak form of the conservation laws, the framework circumvents the limits associated with strong-form discontinuities. This approach ensures entropy consistency while achieving high-resolution shock capturing in discontinuous regions. Due to the inherent dissipation of the modeling approach, the interface thickness tends to increase over time during flow evolution, which degrades the prediction accuracy of the model. To address this limitation, an improved loss function with interface anti-diffusion properties is proposed to effectively suppress interface smearing and enhance prediction fidelity. Through training and extrapolative prediction on various one-dimensional Riemann problems and high-dimensional shock cases, the proposed multiphase PINN model demonstrates accurate interface tracking and high precision in discontinuous regions. The multiphase PINN model developed in this study offers a novel predictive framework for a broad range of compressible multiphase flow problems.