Graph Rewiring based on Flow Alignment for Improving Fluid Simulation

To overcome the computational burden of traditional computational fluid dynamics (CFD), graph neural network-based (GNN) learned simulators have attracted growing interest because they naturally operate on CFD meshes. However, classical GNNs only exchange information between neighbouring nodes, limiting flow prediction accuracy. While graph rewiring can improve information propagation, existing methods are mostly designed for generic graphs, and PIORF relies on long-range connections for fluid simulation. In this work, we show that simply connecting all 2-hop nodes can already achieve competitive performance with PIORF, raising questions about the necessity of distant rewiring. Motivated by fluid transport principles, we propose Flow Alignment Rewiring (FLARE), a simple and efficient local rewiring method that connects 2-hop nodes only when their relative direction aligns with the input flow direction. Hence, FLARE is a physics-informed local rewiring method, different from PIORF and well-aligned with fluid physics. Extensive numerical experiments on flows over a cylinder, single-, and tandem-airfoil under different flow conditions and deep network architectures demonstrate that FLARE outperforms PIORF and various 2-hop rewiring approaches by a significant margin.

Traditional CFD simulations are powerful but often too expensive for repeated engineering use, such as predicting flow around cylinders, airfoils, or multiple interacting bodies. Graph neural networks are promising because they can learn directly on CFD meshes, but standard GNNs only pass information between immediate neighbouring mesh points, which can limit their ability to capture how flow information moves through the domain. Existing graph rewiring methods try to improve this by adding new connections, but they are usually designed for general graph problems rather than fluid flow, and some methods add distant connections whose physical necessity is unclear. We tackle this by asking a simple question: should mesh connections follow the way fluid actually transports information? Based on this idea, we propose Flow Alignment Rewiring (FLARE), which adds only local 2-hop connections when the direction between two mesh points is aligned with the input flow direction. This makes the model’s message passing more consistent with directional fluid transport, without relying on long-range graph connections. Our results show that FLARE improves learned flow prediction across cylinder, single-airfoil, and tandem-airfoil cases, and works with different neural network architectures. This matters because it offers a simple, physically motivated way to make GNN-based CFD simulators more accurate and efficient for practical flow prediction tasks.