Porous absorber

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Figure 1: Sketch of the geometry. The porous material is marked in blue, the acoustic source by $q$.

Figure 2: Frequency response function.

Description

The Porous absorber benchmark models the sound pressure in a cavity excited by a single harmonic load. One side of the cavity is covered by a layer of poroelastic material, which adds dissipation to the system. The geometry of this model follows . Various projection-based model order reduction methods have been applied and compared using this example as a benchmark in .

The cavity has the dimensions $0.75 \times 0.6 \times 0.4\,\mathrm{m}$ and one wall is covered by a $0.05\,\mathrm{m}$ thick poroelastic layer acting as a sound absorber. The poroelastic material is described by the Biot theory and the system is excited by a point source located in a corner opposite of the porous layer. The material parameters for the acoustic fluid and the poroelastic material have been chosen according to.

Dimensions

System structure:

$\begin{align} \left( A_1 + \tilde{\gamma}(s) A_2 + \tilde{\rho}_f(s) A_3 + s^2 A_4 + s^2 \tilde{\gamma}(s) A_5 + s^2 \tilde{\rho}(s) A_6 + \frac{s^2 \phi^2}{\tilde{R}(s)} A_7 \right) x(s) &= B, \\ y(s) &= C x(s), \end{align}$

with the frequency dependent functions for the effective densities $\tilde{\rho}(s), \tilde{\rho}_f(s)$, the parameter $\tilde{\gamma}(s)$ relating the effective densities and the frequency dependent elasticity coefficients to the porosity, and the scaled effective bulk modulus $\tilde{R}(s)$. For more details on the functions, see .

System dimensions:

$A_i, \in \mathbb{R}^{n \times n}$, with $i=1, \ldots, 7$, $B \in \mathbb{R}^{n \times 1}$, $C \in \mathbb{R}^{1 \times n}$, with $n=386\,076$.

Data

The data is available at Zenodo.