Special short wave elements for flow acoustics

A numerical formulation based on the Partition of Unity Method (PUM) is proposed for modelling the propagation of short acoustic waves on irrotational mean flows. The method seeks to reduce the pollution error which exists in conventional FE schemes at high frequencies by using a local basis which is enriched by plane wave solutions of the convected Helmholtz equation. Initially the method is demonstrated with reference to a one dimensional model consisting of a variable area converging-diverging duct with mean flow. Next a simple two-dimensional model of a straight duct with uniform flow, is considered. In both cases the accuracy and the conditioning of the numerical solution is investigated for ranges of frequency and Mach number characteristic of aero-engine bypass ducts.