### Porous Materials; Applications and Engineering Models  
Within this contribution, we focus on the investigation of generic porous materials and their behavior as acoustic absorbers. Porous materials are a well-known measure used to reduce acoustic energy, e.g., as sound absorbers in room acoustics and environmental noise applications [3; 4; 5], porous liners in aircraft engines and airframe [6; 7; 8] and the reduction of trailing edge noise [9; 10; 11], to name a few. Moreover, porous materials can be employed to generate meta-structures and meta-materials. The construction of meta-structures by embedding inclusions into a porous base material is a promising approach to improve the acoustic properties of the base material, as shown in [12; 13]. A comprehensive summary of similarities and differences between porous materials and meta-materials is given in [14]. Further recent examples of meta-materials are shown in [15; 16; 17]. The widespread applications of porous materials motivates the aim to incorporate them in acoustic simulations. Therefore, material models are required. The material models describing the acoustic behavior of porous materials are hereafter referred to as acoustic models.  
In the past, many acoustic models of different complexity for porous materials have been proposed. Starting from the fully empirical models proposed by [PERSON] & Bazley [18] and the subsequent improvement by [PERSON] [19], a range of models based on the idealization of a homogenized material have been established. Therefore, the Biot model [20; 21] is the most complex one and is accepted as the reference [22]. The Biot model considers three types of traveling waves in the material: one pressure wave in the fluid phase and one pressure and one shear wave in the solid phase. Accordingly, both the fluid phase and the solid phase (skeleton) of the porous material are assumed to be elastic. Based on the Biot model, several subsequent models have been proposed that assume the solid phase to be rigid, i.e., modeling only one pressure wave in an equivalent fluid. Therefore, the properties of the equivalent fluid also account for the influence of the skeleton on the wave propagation in the fluid phase. These models are accordingly named equivalent fluid models. Well-known models are the Miki model [23], the model of Champoux-Allard [24] and its extensions, the Johnson-Champoux-Allard (JCA) model [25] the Johnson-Champoux-Allard-Lafarge (JCAL) model [26] and the Johnson-Champoux-Pride-Allard-Lafarge (JCPAL) model [27]. All the aforementioned models require a number of model parameters; for the class of equivalent fluid models, these are (a subset of, depending on the specific model) the flow resistivity \(\Xi\), the porosity \(\Phi\), the tortuosity \(\alpha_{\infty}\), the thermal and viscous characteristic lengths \(\Lambda,\Lambda^{\prime}\), respectively and the static thermal permeability and tortuosity, \(k^{\prime}_{0}\) and \(a^{\prime}_{0}\), respectively. It should be noted that in most literature, the flow resistivity is denoted with the symbol \(\sigma\). For the sake of consistency with our last publications, we choose the letter \(\Xi\) here. Additionally, the Biot model requires the elastic parameters of the skeleton phase as well.