Non-reflecting boundary conditions for acoustic propagation in ducts with acoustic treatment and mean flow

We consider a time-harmonic acoustic scattering problem in a 2D infinite waveguide with walls covered with an absorbing material, in the presence of a mean flow assumed uniform far from the source. To make this problem suitable for a finite element analysis, the infinite domain is truncated. This paper concerns the derivation of a non-reflecting boundary condition on the artificial boundary by means of a Dirichlet-to-Neumann (DtN) map based on a modal decomposition. Compared with the hard-walled guide case, several difficulties are raised by the presence of both the liner and the mean flow. In particular, acoustic modes are no longer orthogonal and behave asymptotically like the modes of a …