In this paper we develop and study numerically a model to describe some aspects of sound propagation in the human lung, considered as a deformable and viscoelastic porous medium (the parenchyma) with millions of alveoli filled with air. Transmission of sound through the lung above 1 kHz is known to be highly frequency-dependent. We pursue the key idea that the viscoelastic parenchyma structure is highly heterogeneous on the small scale ε and use two-scale homogenization techniques to derive effective acoustic equations for asymptotically small ε. This process turns out to introduce new memory effects. The effective material parameters are determined from the solution of frequency-dependent micro-structure cell problems. We propose a numerical approach to investigate the sound propagation in the homogenized parenchyma using a Discontinuous Galerkin formulation. Numerical examples are presented.
Mots-clés : mathematical modeling, periodic homogenization, viscoelastic media, fluid-structure interaction, discontinuous Galerkin methods
@article{M2AN_2014__48_1_27_0,
author = {Cazeaux, Paul and Hesthaven, Jan S.},
title = {Multiscale modelling of sound propagation through the lung parenchyma},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {27--52},
publisher = {EDP-Sciences},
volume = {48},
number = {1},
year = {2014},
doi = {10.1051/m2an/2013093},
mrnumber = {3177836},
zbl = {1285.93014},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2013093/}
}
TY - JOUR AU - Cazeaux, Paul AU - Hesthaven, Jan S. TI - Multiscale modelling of sound propagation through the lung parenchyma JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2014 SP - 27 EP - 52 VL - 48 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2013093/ DO - 10.1051/m2an/2013093 LA - en ID - M2AN_2014__48_1_27_0 ER -
%0 Journal Article %A Cazeaux, Paul %A Hesthaven, Jan S. %T Multiscale modelling of sound propagation through the lung parenchyma %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2014 %P 27-52 %V 48 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2013093/ %R 10.1051/m2an/2013093 %G en %F M2AN_2014__48_1_27_0
Cazeaux, Paul; Hesthaven, Jan S. Multiscale modelling of sound propagation through the lung parenchyma. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 1, pp. 27-52. doi : 10.1051/m2an/2013093. http://www.numdam.org/articles/10.1051/m2an/2013093/
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