A reduced finite element model for sound propagation in straight and slowly varying cross section ducts

Abstract

Finite Element based methods are of interest when the analytical solution for a waveguide cross section is not available. In this work, efforts are made towards the reduction of the Finite Element models size for duct acoustics. The Galerkin Finite Element formulation is used for a local elementary modelling of a uniform duct with mean flow. For the slowly varying cross section ducts, wavenumbers are found locally by means of an eigenvalue problem and the net change of amplitudes between two points along a propagation axis provides finally, through conservation of the time-averaged energy, the solutions for the propagating waves. Although this does not take into consideration the eventual reflection throughout the varying cross section part, it can be used when the cross section variation is slow and its analytical solution is not available. Should speed in the first place be sought, the approach is satisfactory when models are important in size. Accuracy and speed of the approach are discussed while comparing versus an actual full Finite Element modelling. • Finite Element Modelling is used locally. • The slowly varying amplitudes are expressed through an energy evaluation. • The computing time reduction is satisfactory when the models are important in size.