A Novel Physics-Informed Graph Convolutional Reduced-Order Model for Fluid Flow on Unstructured Meshes
This study proposes a physics-informed graph convolutional reduced-order model, namely Phys-GCN, for high-fidelity and computationally efficient prediction of steady incompressible flow fields. In Phys-GCN, the incompressible Navier–Stokes equations are embedded into the loss function via residual constraints, such that the spatial feature extraction of graph convolutional networks is integrated with the physics-constrained learning strategy of physics-informed neural networks. This mixed design enables the model to capture complex nonlinear flow features while maintaining a clear level of physical interpretability. Benefiting from the node-edge encoding inherent to graph neural networks, Phys-GCN operates directly on unstructured CFD meshes to learn flow features from graph representations constructed using node attributes and adjacency relationships. In doing so, Phys-GCN dispenses with voxelization or SDF preprocessing and fully preserves the local geometric and topological characteristics of the flow domain. The proposed model is systematically evaluated on steady flows past circular and elliptical cylinders, where the predicted velocity and pressure fields are compared against reference CFD solutions in both interpolation and extrapolation scenarios. Results show that, for all physical quantities, the reconstructed steady flow fields achieve mean relative errors below 5%, exhibiting excellent agreement with the CFD benchmark solutions. After offline training, Phys-GCN achieves inference times that are several orders of magnitude faster than conventional CFD solvers, while maintaining comparable predictive accuracy. These findings demonstrate that Phys-GCN provides an accurate and efficient graph-based and physics-informed surrogate for steady flow-field reconstruction on non-uniform, unstructured meshes, thereby laying a solid foundation for future extensions to more complex three-dimensional and compressible flow configurations.