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Article Dans Une Revue ESAIM: Mathematical Modelling and Numerical Analysis Année : 2023

A homogenized model accounting for dispersion, interfaces and source points for transient waves in 1D periodic media

R Cornaggia

Résumé

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.
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Dates et versions

hal-03652455 , version 1 (26-04-2022)
hal-03652455 , version 2 (24-03-2023)

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R Cornaggia, Bruno Lombard. A homogenized model accounting for dispersion, interfaces and source points for transient waves in 1D periodic media. ESAIM: Mathematical Modelling and Numerical Analysis, 2023, 57 (3), pp.1413-1444. ⟨10.1051/m2an/2023027⟩. ⟨hal-03652455v2⟩
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