Prediction of Steady and Unsteady Flow Quantities Using Multiscale Graph Neural Networks

Analysis, optimization, and uncertainty quantification of the aerodynamic behavior of turbomachinery components is a fundamental part of the current industrial design process and requires the extensive use of compute-intensive computational fluid dynamics (CFD) simulations. This paper explores the potential of graph neural networks as surrogate models to accelerate the design process, for example, in a multi-fidelity framework. Graph neural networks promise to provide good estimates of flow quantities while maintaining the geometric accuracy at a fraction of the computational effort of CFD. To assess the performance of such methods, a state-of-the-art graph neural network is applied to a turbomachinery setup of industry-relevant mesh size. In particular, a multiscale graph neural network is used to overcome the problems of large information distances when applying message-passing based graph-net blocks to large meshes. The training database consists of a space-filling design of experiment of 100 CFD solutions with different geometries. The first use case encompasses the prediction of flow quantities of the complete fluid domain with $2.5×106$ mesh points. The second use case focuses on predicting a single scalar (e.g., pressure) on surface meshes with up to $30×103$ mesh points. In both cases, the networks predict time-averaged and unsteady flow fields on unstructured meshes of variable point sizes for new geometries not present in the training set. The results demonstrate the proficiency of the approach in predicting time-averaged and unsteady flow quantities on surfaces as well as for full fluid domains for new geometries.