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arXiv · 1309.6666

Two-dimensional wave propagation in layered periodic media

Manuel Quezada de Luna·David I. Ketcheson
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Abstract

We study two-dimensional wave propagation in materials whose properties vary periodically in one direction only. High order homogenization is carried out to derive a dispersive effective medium approximation. One-dimensional materials with constant impedance exhibit no effective dispersion. We show that a new kind of effective dispersion may arise in two dimensions, even in materials with constant impedance. This dispersion is a macroscopic effect of microscopic diffraction caused by spatial variation in the sound speed. We analyze this dispersive effect by using high-order homogenization to derive an anisotropic, dispersive effective medium. We generalize to two dimensions a homogenization approach that has been used previously for one-dimensional problems. Pseudospectral solutions of the effective medium equations agree to high accuracy with finite volume direct numerical simulations of the variable-coefficient equations.

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Manuel Quezada de Luna, David I. Ketcheson. 2013-09-25. Two-dimensional wave propagation in layered periodic media. https://arxiv.org/abs/1309.6666

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