Accelerating Thermal Homann Flow Simulation With Mesh-Based Graph Neural Networks

The numerical simulation of Homann flow, a classical problem in fluid dynamics involving axisymmetric flow over a solid plate, is essential for understanding various boundary layer phenomena. Due to the prominence of this flow and its computationally intensive nature when dealing with turbulent regimes in complex geometries, the present paper explores the use of machine learning (ML) to solve Homann flow with heat transfer both rapidly and accurately. However, the application of ML, especially deep learning (DL), to engineering-focused physics simulations remains a significant challenge. Traditional numerical approaches have consistently demonstrated higher accuracy in simulation tasks compared to DL models, which often suffer from a lack of generalizability when predicting outcomes for geometries that differ slightly from those used in training. In this study, Graph Neural Networks (GNNs) are employed to solve thermal Homann flow on substrates of various geometries. We demonstrate that the trained model accurately predicts outcomes even on entirely novel cases, and notably, the computational efficiency of the GNN model significantly surpasses that of conventional numerical solvers.