Fast Computation of the Scattering Matrix of Lined Ducts Containing Passive Components
Résumé
This paper deals with strategiesfor computing efficiently the propagation ofsound waves in lined ducts containing
passive components. In most cases of practical interest, these added acoustics components can be modelled as
acoustic cavities which are connected to the duct and can be either purely reactive or dissipative. The assessment
of the efficiency of such a system requires a precise knowledge of the acoustic field in the duct. In the present
work a new numerical procedure that judiciously exploit the benefit of the FEM and the mode matching approach
is presented. First, a set of FE eigenmode are computed in the cavity to produce a numerical impedance matrix
connecting the pressure and the acoustic velocity on the duct wall interface. Then an integral representation for
the acoustic pressure in the main duct is used. The presence of acoustic liners on the walls of the duct is taken
into account via an appropriate modal decomposition of the Green’s function. Typical applications involving
Helmholtz resonators and side branch ducts (Herschel-Quincke tubes) are presented. We show that our algorithm
allows a very fast and accurate computation of the scattering matrix of such a system with a numerical complexity
that grows very mildly with the frequency.