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