| Issue |
ESAIM: M2AN
Volume 57, Number 3, May-June 2023
|
|
|---|---|---|
| Page(s) | 1413 - 1444 | |
| DOI | https://doi.org/10.1051/m2an/2023027 | |
| Published online | 18 May 2023 | |
A homogenized model accounting for dispersion, interfaces and source points for transient waves in 1D periodic media
1
Sorbonne Université, CNRS, Institut ∂’Alembert, UMR 7190, Paris, France
2
Aix-Marseille Univ, CNRS, Centrale Marseille, LMA UMR 7031, Marseille, France
* Corresponding author: lombard@lma.cnrs-mrs.fr
Received:
26
April
2022
Accepted:
23
March
2023
A homogenized model is proposed for linear waves in 1D microstructured media. It combines second-order asymptotic homogenization (to account for dispersion) and interface correctors (for transmission from or towards homogeneous media). A new bound on a second-order effective coefficient is proven, ensuring well-posedness of the homogenized model whatever the microstructure. Based on an analogy with existing enriched continua, the evolution equations are reformulated as a dispersive hyperbolic system. The efficiency of the model is illustrated via time-domain numerical simulations. An extension to Dirac source terms is also proposed.
Mathematics Subject Classification: 35F45 / 74J10 / 74Q10
Key words: Waves in periodic media / High-order homogenization / Effective transmission conditions
© The authors. Published by EDP Sciences, SMAI 2023
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