Long-term prediction of cylinder water entry flow fields using a physics-informed spatiotemporal graph neural network

This study introduces a novel physics-informed spatiotemporal graph neural network (PIST-GNN) for rapid, physically consistent, and accurate long-term prediction of complex water entry flow fields. The model integrates a MeshGraphNet-based GNN for spatial feature extraction on unstructured meshes and a long short-term memory (LSTM) network for temporal evolution, critically enhanced by embedding mass conservation and volume of fluid (VOF) transport equations as soft constraints during training. Comprehensive evaluations demonstrate that the combined physics constraints provide an optimal balance, achieving robust predictions with only a slight increase in data loss while significantly reducing physical inconsistencies like velocity divergence and VOF advection residuals. The PIST-GNN exhibits superior long-term stability and generalization capabilities, consistently maintaining the lowest prediction errors and the best physical consistency over 30 autoregressive steps on unseen Froude number and initial angle cases. Furthermore, through both quantitative and qualitative analysis of prediction results, we elucidate the complex influence of initial conditions on prediction accuracy. Ultimately, this study provides a practical and feasible approach to address the persistent challenge of error accumulation in long-term predictions of water entry flow fields by purely data-driven models. Future research will focus on overcoming the limitations of the current two-dimensional slice approximation method by optimizing physical constraints and model architecture, thereby more directly capturing the complete three-dimensional dynamic characteristics of the water entry flow field.