Discontinuous Galerkin method for the computation of acoustic modes in lined flow ducts with rigid splices

A discontinuous Galerkin method for the discretisation of the linearised Euler equations is derived for the computation of acoustic modes in an infinite duct of arbitrary geometric shape in the presence of axial sheared flow. Validations are performed with analytical solutions in the case of a uniformly lined duct and comparisons are done with the literature in the case of a lined cylindrical duct with rigid splices. We take advantage of the discontinuous formulation to study the behaviour of the acoustic eigenfunctions in the vicinity of the liner-splice transition where singular behaviours of the acoustic perturbation are found.