A time domain equivalent fluid model for the acoustic wave equation

Acoustically absorbing materials such as acoustic foam can be described by the equivalent fluid model.
The homogenized fluid's acoustic behavior is thereby described by complex-valued, frequency-
dependent material parameters (equivalent density and compression modulus). In this case, convolution
integrals of the material parameters and the acoustic pressure arise when the acoustic wave equation is
transformed from frequency to time domain. We circumvent the numerically demanding calculation of
these integrals by introducing auxiliary differential equations (ADEs), which are coupled to the wave
equation according to the ADE method. The set of coupled differential equations is solved using the
finite element method (FEM). The methodology requires the equivalent fluid parameters to be modeled
by a rational function representing the frequency-dependent material behavior (frequency response
function - FRF). Thereby, the order of the FRF defines the number of additionally introduced ADEs
and auxiliary variables. The derivation of the formulation is presented, and validation examples are
shown.