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Mercier JF, Maurel A. Improved multimodal method for the acoustic propagation in waveguides with a wall impedance and a uniform flow. Proc Math Phys Eng Sci. 2016;472(2190):20160094doi: 10.1098/rspa.2016.0094.
Mercier, J. F., & Maurel, A. (2016). Improved multimodal method for the acoustic propagation in waveguides with a wall impedance and a uniform flow. Proceedings. Mathematical, physical, and engineering sciences, 472(2190), 20160094. https://doi.org/10.1098/rspa.2016.0094
Mercier, Jean-François, and Maurel, Agnès. "Improved multimodal method for the acoustic propagation in waveguides with a wall impedance and a uniform flow." Proceedings. Mathematical, physical, and engineering sciences vol. 472,2190 (2016): 20160094. doi: https://doi.org/10.1098/rspa.2016.0094
Mercier JF, Maurel A. Improved multimodal method for the acoustic propagation in waveguides with a wall impedance and a uniform flow. Proc Math Phys Eng Sci. 2016 Jun;472(2190):20160094. doi: 10.1098/rspa.2016.0094. PMID: 27436978; PMCID: PMC4950203.
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Proc Math Phys Eng Sci. 2016 Jun;472(2190):20160094. doi: 10.1098/rspa.2016.0094.

Improved multimodal method for the acoustic propagation in waveguides with a wall impedance and a uniform flow.

Proceedings. Mathematical, physical, and engineering sciences

Jean-François Mercier, Agnès Maurel

Affiliations

  1. POEMS, ENSTA ParisTech, CNRS, Inria , Université Paris-Saclay , 828 bd des Maréchaux, 91762 Palaiseau Cedex, France.
  2. Institut Langevin , CNRS, ESPCI ParisTech, 1 rue Jussieu, 75005 Paris, France.

PMID: 27436978 PMCID: PMC4950203 DOI: 10.1098/rspa.2016.0094

Abstract

We present an efficient multimodal method to describe the acoustic propagation in the presence of a uniform flow in a waveguide with locally a wall impedance treatment. The method relies on a variational formulation of the problem, which allows to derive a multimodal formulation within a rigorous mathematical framework, notably to properly account for the boundary conditions on the walls (being locally the Myers condition and the Neumann condition otherwise). Also, the method uses an enriched basis with respect to the usual cosine basis, able to absorb the less converging part of the modal series and thus, to improve the convergence of the method. Using the cosine basis, the modal method has a low convergence, 1/

Keywords: acoustics in flows; modal methods; multiple scattering; time harmonic

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