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 modeling for fluid flow with the mesh corotating with the structure. Unlike conventional data-driven approaches that rely on structured Cartesian meshes, our framework operates on unstructured co-rotating meshes, enforcing rotation equivariance of the learned model by leveraging co-rotating polar (2D) and cylindrical (3D) coordinate systems. To model the pressure for systems without Dirichlet pressure boundaries, we propose a novel local directed pressure difference formulation that is invariant to the reference pressure point and value. For flow systems with large mesh sizes, we introduce a scheme to train the network in single or distributed graphics processing units by accumulating the backpropagated gradients from partitions of the mesh. The effectiveness of our proposed framework is examined on two test cases: (i) fluid flow in a 2D rotating mixer, and (ii) the flow past a 3D rotating cube. Our results show that the model achieves stable and accurate rollouts for over 2000 time steps in periodic regimes while capturing accurate short-term dynamics in chaotic flow regimes. In addition, the drag and lift force predictions closely match the CFD calculations, highlighting the potential of the framework for modeling both periodic and chaotic fluid flow around rotating structures.

翻译：图神经网络作为流体流动代理建模领域的新兴方法，已成功应用于多种流动系统的时间演化建模。然而，现有应用大多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的流体流动问题。具体而言，我们提出采用基于图神经网络的代理建模方法，对网格随结构共同旋转的流动进行建模。与依赖结构化笛卡尔网格的传统数据驱动方法不同，本框架在非结构化的共旋转网格上运行，通过采用共旋转极坐标系（二维）与圆柱坐标系（三维），确保学习模型具有旋转等变性。针对无狄利克雷压力边界条件的系统，我们提出了一种新颖的局部定向压力差公式，该公式对参考压力点与参考值具有不变性。对于大规模网格的流动系统，我们引入了一种通过在网格分区上累积反向传播梯度，在单块或多块图形处理器上进行网络训练的方案。通过两个测试案例验证了所提框架的有效性：（i）二维旋转混合器内的流体流动；（ii）绕三维旋转立方体的流动。结果表明：在周期性流态中，模型能实现超过2000个时间步的稳定精确推演；在混沌流态中，模型能准确捕捉短期动力学特征。此外，模型预测的阻力与升力与计算流体力学结果高度吻合，凸显了该框架在模拟旋转结构周围周期性流动与混沌流动方面的潜力。