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

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.