60 research outputs found
Two-dimensional wave propagation in layered periodic media
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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