A development on fast frequency sweep methods for acoustic radiation problems

The direct point by point swept solution of the discretised Helmholtz equation over a broad frequency range can become computationally expensive for large systems when fine frequency increments are required. Approaches involving reduced-order models using Padéor waveform-based methods such as the well conditioned asymptotic waveform evaluation (WCAWE) can be used to significantly reduce this and can also be applied to systems with non-quadratic frequency dependency. In this paper WCAWE expansions are performed on a finite element based dynamical model of a two microphone open flanged impedance tube test. The use of an approximate loss-factor-based PML type approach to model the radiating section of the system is considered which eliminates dependency on reciprocal frequency terms. This allows for an efficient high order expansion as the frequency derivative terms need to be retained only up to second order. It is then shown that the method efficiently gives robust predictions of the end impedance with simple non-specialized elements.