Addressing variable mesh challenges: Generalizable supersonic flow field density prediction via graph neural networks

Unstructured meshes offer the flexibility to capture complex details in flow fields, and graph neural networks (GNNs) are regarded as a natural tool for processing such mesh data. However, in practical flow field simulations, the topology of computational meshes changes with variations in aircraft geometry and flight conditions. When confronted with such fundamental topological variations, the predictive performance of existing GNN methods declines significantly, severely limiting their ability to generalize to unseen mesh topologies. To address this challenge, we propose a graph convolution method based on a geometric attention mechanism, which integrates a learnable local flow direction encoding and a cosine similarity weighting strategy to actively learn geometric relational rules that are independent of specific mesh connectivity. This approach enhances feature extraction and representation in flow fields, maintains stable performance across different mesh structures, and improves the capture of high-gradient features such as shock waves. As a result, the model's robustness to mesh topological changes and its predictive accuracy are significantly improved. Numerical experiments on several typical supersonic flow cases demonstrate that, compared to existing GNN methods, the proposed approach achieves superior performance in both accuracy and generalization capability, effectively adapting to topological variations in unstructured meshes.