Numerical simulation of acoustic waves in air and porelastic media using the partition of unity finite element method

Abstract

Foams and fibrous materials are used in a large range of applications such as automotive or building acoustics. Their properties can be described with either a poroelastic model or an equivalent fluid model. These models, also used in geophysics, are now widely spread and are also available in some commercial finite element software applications. However the discretization level required to achieve reasonable accuracy is not always acceptable in the mid-frequency range. In such case, the Partition of Unity Finite Element Method (PUFEM) using plane wave functions seems appropriate to avoid this limitation. The PUFEM has been recently applied to rigid frame materials with and without coupling with an acoustic cavity. It has also been applied efficiently to poroelastic materials. The present work focuses on the coupling between a poroelastic material, i.e. described with Biot's equations, and an air cavity. Some practical examples are tested to demonstrate the efficiency of the PUFEM for solving noise control problems at medium frequency, but also to underline the precautions that must be taken when dealing with an air-porous interface.