The present paper is the numerical counterpart of a recently published experimental investigation by Wood et al. (2018). Both studies aim at the investigation of instantaneous fluid–structure interaction (FSI) phenomena observed for an air-inflated flexible membrane exposed to a turbulent boundary layer, but looking at the coupled system based on different methodologies. The objective of the numerical studies is to supplement the experimental investigations by additional insights, which were impossible to achieve in the experiments. Relying on the large-eddy simulation technique for the predictions of the turbulent flow, non-linear membrane elements for the structure and a partitioned algorithm for the FSI coupling, three cases with different Reynolds numbers (Re=50,000, 75,000 and 100,000) are simulated. The time-averaged first and second-order moments of the flow are presented as well as the time-averaged deformations and standard deviations. The predictions are compared with the experimental references data solely available for 2D planes. In order to better comprehend the three-dimensionality of the problem, the data analysis of the predictions is extended to 3D time-averaged flow and structure data. Despite minor discrepancies an overall satisfying agreement concerning the time-averaged data is reached between experimental data in the symmetry plane and the simulations. Thus for an in-depth analysis, the numerical results are used to characterize the transient FSI phenomena of the present cases either related to the flow or to the structure. Particular attention is paid to depict the different vortex shedding types occurring at the top, on the side and in the wake of the flexible hemispherical membrane. Since the fluid flow plays a significant role in the FSI phenomena, but at the same the flexible membrane with its eigenmodes also impacts the deformations, the analysis is based on the frequencies and Strouhal numbers found allowing to categorize the different observations accordingly.