Domain decomposition method based on One-Way approaches for sound propagation in a partially lined duct

A numerical factorization method of the unidirectional propagation operators induced by the linearized Euler and Navier–Stokes equations is performed to construct a new One-Way approach to compute the sound radiation in a partially lined duct. The complex phenomena of reflection and transmission of incident waves originating from discontinuities in the duct wall are accurately taken into account by an iterative domain decomposition method. Furthermore, the proposed factorization approach allows both the derivation of the lined duct scattering matrix and an in-depth understanding of the impact of the acoustic liner on left- and right-going waves coming from a transmission or a reflection. Finally, the efficiency of the numerical method is shown based on a classical benchmark with two types of baseflows (laminar and turbulent Poiseuille flows) and by comparison with other numerical and experimental results. An unstable surface mode is observed at 1000 Hz, and we find good agreement with experimental data for the turbulent mean flow associated with the One-Way Navier–Stokes equations.