A Mesh-Adaptive Hypergraph Neural Network for Unsteady Flow Around Oscillating and Rotating Structures

TL;DR

This work addresses the challenge of modeling unsteady flow around rotating structures by introducing a mesh-adaptive hypergraph neural network that partitions the domain into a co-rotating and a static region connected by an adaptive interface. A finite-element–inspired $oldsymbol{ ext{phi}}$-GNN operates on a hypergraph representation to evolve state features with time, while a reconstruction and re-projection scheme maintains accuracy across mesh distortions due to rotation; predictions are kept rotation-equivariant through careful feature design. The framework delivers stable long-time rollouts for 2D and 3D test cases and can achieve accurate, error-bounded results when sparse pressure sensors are incorporated, including close agreement on lift and drag with CFD. This approach advances efficient, physics-aware surrogate modeling for rotating-fluid systems and lays groundwork for complex setups like marine propellers and turbines with potential real-time control and design optimization implications.

Abstract

Graph neural networks, recently introduced into the field of fluid flow surrogate modeling, have been successfully applied to model the temporal evolution of various fluid flow systems. Existing applications, however, are mostly restricted to cases where the domain is time-invariant. The present work extends the application of graph neural network-based modeling to fluid flow around structures rotating with respect to a certain axis. Specifically, we propose to apply a graph neural network-based surrogate model with part of the mesh/graph co-rotating with the structure and part of the mesh/graph static. A single layer of interface cells are constructed at the interface between the two parts and are allowed to distort and adapt, which helps in circumventing the difficulty of interpolating information encoded by the neural network at every graph neural network layer. Dedicated reconstruction and re-projection schemes are designed to counter the error caused by the distortion and connectivity change of the interface cells. The effectiveness of our proposed framework is examined on two test cases: (i) fluid flow around a 2D oscillating airfoil, and (ii) fluid flow past a 3D rotating cube. Our results show that the model achieves stable rollout predictions over hundreds or even a thousand time steps. We further demonstrate that one could enforce accurate, error-bounded prediction results by incorporating the measurements from sparse pressure sensors. In addition to the accurate flow field predictions, the lift and drag force predictions closely match with the computational fluid dynamics calculations, highlighting the potential of the framework for modeling fluid flow around rotating structures, and paving the path towards a graph neural network-based surrogate model for more complex scenarios like flow around marine propellers.

Figures (15)

• Figure 1: (a) Schematic of the system domain $\Omega$ which contains a rotating solid body, (b) conversion from a computational mesh to a node-element hypergraph, and (c) schematic of the element and node update stages within each hypergraph message-passing layer in $\phi$-GNN.
• Figure 2: Schematic of the construction and adaptation of the interface cells. (a) Initial construction of the cells. (b) Rotation of the solid body leads to some distortion of the cells, as mismatch angle $\theta_m$ is smaller than the limit $\theta_a$ no mesh adaptation is performed. (c) Further solid body rotation cause more distortion of the cells, triggering the mesh adaptation, leading to the new interface cells in (d).
• Figure 3: (a) Schematic of the data flow of the graph neural network for cases with time-invariant meshes with $\phi$-GNN in gao2024finite. (b) Schematic of the data flow for the current framework.
• Figure 4: Schematic of geometry and flow feature transformations for 2D case: (a) a (quadrilateral) element $\square$ connecting four nodes, (b) the geometry features used, and (c) projection of flow velocity $(u_{x,i},u_{y,i})$ onto the direction of the local coordinates of the element-node edges. Figure modified from Fig. 4 in gao2024finite.
• Figure 5: Schematic indicating the used and discarded element-node edge features in the nodal velocity and pressure reconstruction process.

Theorems & Definitions (2)

• Remark 1
• Remark 2