On the numerical accuracy of a combined fem/radiating-surface approach for noise propagation in unbounded domains

Abstract

The focus of this study is to present the limitations of a hybrid numerical method for the prediction
of sound propagation and scattering within an unbounded domain. We present a combined
Finite Element Method (FEM)/Radiating-surface approach based on a Kirchhoff’s integral formulation
with a mean flow. This work identifies the sources of numerical error inherent to the
hybrid method. A potential formulation is adopted for wave propagation and the problem is set
in the frequency domain. The finite element method is applied to solve the scattering problem
in presence of non-uniformities. The FEM solution, combined with a Perfectly Matched Layer
(PML), is mapped on a closed surface. The Kirchhoff’s radiating surface with a uniform mean
flow propagates acoustic waves in free field. The problem of radiation from a monopole source
and the scattering by a cylinder from the same source are presented as numerical examples by accounting
for a subsonic mean flow. The accuracy in the prediction of the acoustic particle velocity
is critical for the efficacy of the method. The main achievement is that the detrimental effect of
the mean flow on the pollution error can be limited by applying the hybrid method. On the other
hand, the integral formulation is exact only for a uniform mean flow.

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