With the increase in computing power, large eddy simulation (LES) emerges as a promising technique to improve both knowledge of complex physics and reliability of turbomachinery flow predictions. However, these simulations are very expensive for industrial applications, especially when a configuration should be considered. The objective of this paper is thus to adapt the well-known phase-lagged conditions to the LES approach by replacing the traditional Fourier series decomposition (FSD) with a compression method that does not make any assumptions on the spectrum of the flow. Several methods are reviewed, and the proper orthogonal decomposition (POD) is retained. This new method is first validated on a flow around a circular cylinder with rotating downstream blocks. The results show significant improvements with respect to the FSD. It is then applied to unsteady Reynolds-averaged Navier–Stokes (URANS) simulations of a single-stage compressor in 2.5D and 3D as a first validation step toward single-passage LES of turbomachinery configuration.