Improved multimodal admittance method in varying cross section waveguides.
An improved version of the multimodal admittance method in acoustic waveguides with varying cross sections is presented. This method aims at a better convergence with respect to the number of transverse modes that are taken into account. It is based on an enriched modal expansion of the pressure: theNfirst modes are the local transverse modes and a supplementary (N+1)th mode, called boundary mode, is a well-chosen transverse function orthogonal to theNfirst modes. This expansion leads to the classical form of the coupled mode equations where the component of the boundary mode is of evanescent character. Under this form, the multimodal admittance method based on the Riccati equation on the admittance matrix (the Dirichlet-to-Neumann operator) is straightforwardly implemented. With this supplementary mode, in addition to the improvement of the convergence of the pressure field, results show a superconvergence of the scattered field outside of the varying cross sections region.
Institut Langevin, 1 rue Jussieu 75005 Paris, France.
Agnès
A
Maurel
Poems - ENSTA, 828 boulevard des Maréchaux 91762 Palaiseau, France.
Jean-François
JF
Mercier
LAUM - Université du Maine, Avenue O. Messiaen 72085 Le Mans, France.
Vincent
V
Pagneux
boundary mode; impedance matrix; multimodal method; waveguide