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

Marie Touboul , Bruno Lombard (1) , Cédric Bellis (2)

1 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]
2 M&S - Matériaux et Structures

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.

Mots clés: resonant microstructures; resonant effective interfaces; frequency-dependent jump conditions; immersed interface method; ADER scheme

Domaines: Acoustique [physics.class-ph]

Marie Touboul, Bruno Lombard, Cédric Bellis. Time-domain simulation of wave propagation across resonant meta-interfaces. 2019. ⟨hal-02185076v1⟩