Modeling the wall shear stress in large-eddy simulation using graph neural networks

As the Reynolds number increases, the large-eddy simulation (LES) of complex flows becomes increasingly intractable because near-wall turbulent structures become increasingly small. Wall modeling reduces the computa-tional requirements of LES by enabling the use of coarser cells at the walls. This paper presents a machine-learning methodology to develop data-driven wall-shear-stress models that can directly operate, a posteriori, on the unstruc-tured grid of the simulation. The model architecture is based on graph neural networks. The model is trained on a database which includes fully developed boundary layers, adverse pressure gradients, separated boundary layers, and laminar-turbulent transition. The relevance of the trained model is verified a posteriori for the simulation of a channel flow, a backward-facing step and a linear blade cascade.