A computational approach based on extended finite element method for thin porous layers in acoustic problems

Abstract

The simulation of stationary acoustic fields involving thin porous layers is addressed in the present article. Layer thickness is assumed to be relatively thin in comparison to the overall computational domain, but its non‐negligible acoustic impact must be taken into consideration in the numerical model. Within the classical finite element method (FEM), meshes are compatible at material interfaces and the element distortions needs to be avoided. These requirements usually lead to an excessively costly spatial discretization for these problems of interest, as it forces mesh refinement surrounding the thin layer. This article provides a computational approach to relax this restriction. A generalized interface model derived from the plane wave transfer matrix Method (TMM) is established for modeling thin layers. We develop variationally consistent formulations to impose the interface conditions from models of thin layers for diverse coupling configurations, in which both acoustic fluid and poro‐elastic media are taken into account. The computational domain is discretized using the extended finite element method (X‐FEM) in order to introduce strong discontinuities in elements independently of the mesh. Implementation of the proposed formulations within X‐FEM is verified to be capable of providing accurate and robust solutions. The efficiency and flexibility of the present approach for multi‐layer and complex geometry problems are demonstrated compared to classical interface‐fitted finite element models through different simulation scenarios.

XFEM implementation procedure for models involving contribution on interfaces

“…where the matrices [A k L ], L ∈ {S, H} belong to M 6×n gdf and [A k ψ ] ∈ M 24×n gdf , so, thanks to (39), one can assemble the blocks of the elementary matrices separately as…”

“…One can also find applications to accoustics [39], materials science (corrosion) [2] or environmental science [13].…”