In wave propagation, One-Way approaches are efficient tools to keep only waves propagating in a privileged direction. However, the construction of this type of method in aeroacoustics can quickly become complex due to pseudo-differential operators involved. Towne \& Colonius [A. Towne and T. Colonius, J. Comput. Phys., 2015] have overcome this difficulty for slowly varying flows by proposing a purely numerical One-Way method based on a non-reflecting boundary condition [T. Hagstrom and T. Warburton, Wave Motion, 2004] applied to linear hyperbolic problems. We extended the validity domain of this method in [C. Rudel, S. Pernet and J.-P. Brazier, J. Sci. Comput., 2022] by introducing an explicit factorization of the propagation operator. More precisely, by using the non-reflecting boundary condition [T. Hagstrom and T. Warburton, Wave Motion, 2004] twice, it is possible to rigorously identify left-going modes (left invariant space) and right-going modes (right invariant space). This approach based on a full construction of the left and right projection operators allows taking into account reflection and transmission of waves that occur in domains with discontinuities, such as partially lined ducts. Starting from the general One-Way methodology, we will explain in this talk the numerical factorization of the propagation operator, and will see how to apply it to a domain decomposition method. We will then finish with some One-Way simulations (linearized Euler and Navier-Stokes) with applications to ducts containing acoustic liners, a field in which these methods can both enable fast predictions and identify instability mechanisms. The results will be compared to other numerical simulations and experimental measures for a range of frequencies.