Numerical modeling of the acoustic wave propagation across an homogenized rigid microstructure in the time domain

TL;DR

This paper develops a numerical method to simulate acoustic wave propagation across homogenized microstructures with jump conditions, validating the approach by comparing it to real microstructures in the time domain.

Contribution

It introduces an adapted immersed interface method for handling jump conditions in time-domain acoustic simulations involving homogenized microstructures.

Findings

The numerical method accurately simulates wave propagation across complex interfaces.

The homogenized model's validity is confirmed through numerical comparisons.

Efficient handling of arbitrary-shaped interfaces on Cartesian grids.

Abstract

Homogenization of a thin micro-structure yields effective jump conditions that incorporate the geometrical features of the scatterers. These jump conditions apply across a thin but nonzero thickness interface whose interior is disregarded. This paper aims (i) to propose a numerical method able to handle the jump conditions in order to simulate the homogenized problem in the time domain, (ii) to inspect the validity of the homogenized problem when compared to the real one. For this purpose, we adapt an immersed interface method originally developed for standard jump conditions across a zero-thickness interface. Doing so allows us to handle arbitrary-shaped interfaces on a Cartesian grid with the same efficiency and accuracy of the numerical scheme than those obtained in an homogeneous medium. Numerical experiments are performed to test the properties of the numerical method and to inspect the validity of the homogenization problem.