Homogenization of a model for the propagation of sound in the lungs

Paul Cazeaux, Céline Grandmont, Yvon Maday

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

In this paper, we are interested in the mathematical modeling of the propagation of sound waves in the lung parenchyma, which is a foam-like elastic material containing millions of air-filled alveoli. In this study, the parenchyma is governed by the linearized elasticity equations, and the air by the acoustic wave equations. The geometric arrangement of the alveoli is assumed to be periodic with a small period ε > 0. We consider the time-harmonic regime forced by vibrations induced by volumic forces. We use the two-scale convergence theory to study the asymptotic behavior as ε goes to zero and prove the convergence of the solutions of the coupled fluid-structure problem to the solution of a linear-elasticity boundary value problem.

Original languageEnglish (US)
Pages (from-to)43-71
Number of pages29
JournalMultiscale Modeling and Simulation
Volume13
Issue number1
DOIs
StatePublished - 2015

Bibliographical note

Publisher Copyright:
© 2015 Society for Industrial and Applied Mathematics.

Keywords

  • Acoustic-elastic interaction
  • Asymptotic analysis
  • Mathematical modeling
  • Periodic homogenization

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