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.

翻译：图神经网络作为流体流动替代建模领域的新兴工具，已成功应用于多种流体流动系统的时间演化建模。然而，现有应用主要局限于计算域不随时间变化的场景。本研究将基于图神经网络的建模方法拓展至绕固定轴旋转结构周围的流体流动问题。具体而言，我们提出一种基于图神经网络的替代模型，其中部分网格/图随结构共同旋转，其余部分保持静止。在两部分交界面处构建单层界面单元，允许其发生形变与自适应调整，从而规避了在图神经网络每一层对神经网络编码信息进行插值的难题。针对界面单元形变与连接关系变化引起的误差，我们设计了专门的重构与重投影方案。所提框架的有效性通过两个测试案例进行验证：（一）二维振荡翼型绕流；（二）三维旋转立方体绕流。结果表明，该模型能实现数百甚至上千个时间步的稳定滚动预测。我们进一步证明，通过融合稀疏压力传感器的测量数据，可获得误差有界的精确预测结果。除流场预测精度外，升力与阻力预测结果与计算流体动力学计算结果高度吻合，凸显了该框架在旋转结构绕流建模中的应用潜力，并为构建更复杂场景（如船舶螺旋桨绕流）的图神经网络替代模型奠定了基础。