Two-dimensional wave propagation in layered periodic media
For researchers modeling wave propagation in periodic media, this work extends homogenization to 2D and reveals a previously unknown dispersion mechanism, but the contribution is incremental as it generalizes existing 1D methods.
The paper studies 2D wave propagation in layered periodic media, deriving a dispersive effective medium via high-order homogenization. It shows that a new kind of effective dispersion arises in 2D even for constant-impedance materials, and validates the model with pseudospectral solutions matching direct simulations.
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.