Algorithm

Pixel

Laminar flow

Computer graphics (images)

Theoretical computer science

Computation

Computer science

Markov random field

Image segmentation

Physics

Graph

Conditional random field

Pattern recognition (psychology)

Image (mathematics)

Artificial intelligence

Computational fluid dynamics

Polygon mesh

Artificial neural network

Mechanics

Convolutional neural network

Convolution (computer science)

Physics of Fluids

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.

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