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:

$\begin{array}{rl}(K+\tilde{\gamma }(s)K_{p,1}+{\tilde{\rho }}_f(s)K_{p,2}+s^{2}M+s^2\tilde{\gamma }(s)M_{p,1}+s^2\tilde{\rho }(s)M_{p,2}+\frac{s^2{\varphi }^2}{\tilde{R}(s)}{M}_{p,3})x(s)& =B,\\ y(s)& =Cx(s),\end{array}$

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:

$K,K_{p,1},K_{p,2},M,M_{p,1},M_{p,2},M_{p,3}\in {\mathbb{ℝ}}^{n\times n}$, $B\in {\mathbb{ℝ}}^{n\times 1}$, $C\in {\mathbb{ℝ}}^{1\times n}$, with $n=386076$.

Data

The data is available at Zenodo.