Application of Graph Neural Networks in Computational Fluid Mechanics

Abstract

Computational fluid dynamics (CFD) discretizes the Navier-Stokes equations on computational meshes to obtain flow-field quantities like velocity, pressure, and density through numerical iteration, but traditional solvers, though reliable in accuracy, are computationally expensive and time-consuming for high-Reynolds-number turbulence and complex unsteady flows. With geometric deep learning, graph neural networks (GNNs) overcome the limitation of conventional neural network (CNNs) that only handle grid-structured Euclidean data; by message-passing, they naturally fit unstructured CFD meshes and capture spatial correlations. This paper systematically reviews GNN fundamentals and core fluid mechanics, including turbulence characteristics and mesh type classifications, and then focuses on typical GNN applications in flow-field prediction, turbulence modeling, and complex-flow simulation. Existing challenges such as high training costs, insufficient generalization, and limited computational efficiency are analyzed, and promising future research directions are discussed. The review indicates GNNs are efficient surrogates for traditional solvers, offering a pathway to intelligent, fast, high-fidelity simulation.