Design of broadband time-domain impedance boundary conditions using the oscillatory-diffusive representation of acoustical models

Florian Monteghetti (1) , Denis Matignon (2) , Estelle Piot (1) , Lucas Pascal (1)

1 ONERA - The French Aerospace Lab [Toulouse]
2 ISAE-SUPAERO - Institut Supérieur de l'Aéronautique et de l'Espace

A methodology to design broadband time-domain impedance boundary conditions (TDIBCs) from the analysis of acoustical models is presented. The derived TDIBCs are recast exclusively as first-order differential equations, well-suited for high-order numerical simulations. Broadband approximations are yielded from an elementary linear least squares optimization that is, for most models, independent of the absorbing material geometry. This methodology relies on a mathematical technique referred to as the oscillatory-diffusive (or poles and cuts) representation, and is applied to a wide range of acoustical models, drawn from duct acoustics and outdoor sound propagation, which covers perforates, semi-infinite ground layers as well as cavities filled with a porous medium. It is shown that each of these impedance models leads to a different TDIBC. Comparison with existing numerical models, such as multi-pole or extended Helmholtz resonator, provides insights into their suitability. Additionally, the broadly-applicable fractional polynomial impedance models are analyzed using fractional calculus.

Mots clés: aeroacoustics; impedance; time domain

Domaines: Acoustique [physics.class-ph]; Physique Numérique [physics.comp-ph]

Florian Monteghetti, Denis Matignon, Estelle Piot, Lucas Pascal. Design of broadband time-domain impedance boundary conditions using the oscillatory-diffusive representation of acoustical models. Journal of the Acoustical Society of America, 2016, 140 (3), pp.1663 - 1674. ⟨10.1121/1.4962277⟩. ⟨hal-01530759⟩