Graph neural networks for laminar flow prediction around random two-dimensional shapes

In recent years, the domain of fast flow field prediction has been vastly dominated by pixel-based convolutional neural networks. Yet, the recent advent of graph convolutional neural networks (GCNNs) has attracted considerable attention in the computational fluid dynamics (CFD) community. In this contribution, we proposed a GCNN structure as a surrogate model for laminar flow prediction around two-dimensional (2D) obstacles. Unlike traditional convolution on image pixels, the graph convolution can be directly applied on body-fitted triangular meshes, hence yielding an easy coupling with CFD solvers. The proposed GCNN model is trained over a dataset composed of CFD-computed laminar flows around 2000 random 2D shapes. Accuracy levels are assessed on reconstructed velocity and pressure fields around out-of-training obstacles and are compared with that of standard U-net architectures, especially in the boundary layer area.