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Time-domain simulation of wave propagation across resonant meta-interfaces

Abstract : Meta-interface models stem from the homogenization, in a low-frequency dynamic regime, of thin heterogeneous layers that are structured to achieve uncommon properties at the macro-scopic level. When the layer is composed of a thin periodic array of highly-contrasted inclusions embedded within a homogeneous background medium then the corresponding effective interface model is characterized by jump conditions that, in the harmonic regime, involve some singular frequency-dependent terms. In this context, the article is concerned with the simulation of transient waves across such resonant meta-interfaces and a numerical method is proposed to handle the associated resonant jump conditions. To do so, a set of auxiliary variables is introduced locally along the interface and an augmented system of first-order equations in time accompanied with local-in-time jump conditions is derived. This system is then discretized on a Cartesian grid and solved using a high-order finite-difference scheme while the complexity associated with the geometry of the interface and the jump conditions is handled using an immersed interface method. A set of numerical examples in 1D and 2D is proposed to illustrate and validate the overall numerical approach, and quantitative comparisons with semi-analytical solutions are also provided.
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Submitted on : Saturday, April 11, 2020 - 7:35:10 AM
Last modification on : Wednesday, November 3, 2021 - 5:53:18 AM


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  • HAL Id : hal-02185076, version 2


Marie Touboul, Bruno Lombard, Cédric Bellis. Time-domain simulation of wave propagation across resonant meta-interfaces. Journal of Computational Physics, Elsevier, 2020, 414 (1). ⟨hal-02185076v2⟩



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