Transparent boundary condition for acoustic propagation in lined guide with mean flow

Abstract

A finite element analysis of acoustic radiation in an infinite lined guide with mean flow is studied. In order to bound the domain, transparent boundary conditions are introduced by means of a Dirichlet to Neumann (DtN) operator based on a modal decomposition. This decomposition is easy to carry out in a hard‐walled guide. With absorbant lining, many difficulties occur even without mean flow. Since the eigenvalue problem is no longer selfadjoint, acoustic modes are not orthogonal with respect to the L2‐scalar product. However, an orthogonality relation exists which permits writing the modal decomposition. For a lined guide with uniform mean flow, modes are no longer orthogonal but a new scalar product allows us to define the DtN operator. We consider first the case of an infinite rectangular two‐dimensional lined guide with uniform mean flow in order to present the methodology. Then, some extensions will be presented: non‐uniform two‐dimensional geometries by calculating potential mean flow, and cylindrical axisymmetric three‐dimensional problems with uniform mean flow.