## 1 Introduction
The advantage of this method is that it does not require evaluating the particle velocity and the pressure in the material. However, the two-parameter approach requires its comparison with the relaxation model [16], giving an equivalent set of ZK equations. [PERSON] et al. [17], make use of a similar approach, also by means of ZK equations, which modifies Euler and momentum equations to  
\[\rho^{\prime}\frac{\partial\mathbf{u}}{\partial t}+R^{\prime}\mathbf{u}=-\
abla p \tag{7}\]  
\[\frac{1}{\rho^{\prime}c^{\prime}2}\frac{\partial p}{\partial t}=-\
abla\mathbf{u} \tag{8}\]  
where \(\rho^{\prime}=\rho_{0}\text{k}_{\text{s}}/\varphi\), being \(\text{k}_{\text{s}}\) the structure factor, \(\varphi\) porosity, \(\text{c}^{\prime}=\text{c}_{0}/\sqrt{\text{k}_{\text{S}}}\) and \(R^{\prime}\) is the flow resistivity. This is a straightforward approach to describe sound propagation in a porous material, and it exhibits a lower computational cost. The drawback of the model is the difficulty in finding the indicated parameters for each type of simulated material. [PERSON] et al. [18], use the Rayleigh method developed by [PERSON] [19], adding a \"moving frame\" to the constitutive equations that represents the acoustic behavior at low frequencies. At the bottom, the Rayleigh method resembles the initial ZK formulation for porous materials. However, instead of having a homogeneous layer, the material is represented as a set of thin rigid pipes which let the air pass in between [19]. Recently, [PERSON] et al. [20], developed a method where they manage the effective density and the effective compressibility through infinite impulse response (IIR) filters. Temporal convolutions that follow from Equations (25) and (26) in reference [5] are avoided thanks to the use of a Z-transform to the IIR function transfer. Also, to employ this method, it is mandatory to Z-transform the constitutive equations. The material's characteristic impedance is measured then, and from it, all calculations can be performed. [PERSON] et al. [21] describe the porous material propagation in a similar manner as the JCAL model, by using an effective density and effective compressibility, which are expressed in terms of partial fraction expansions. Such an approach forces the use of nine auxiliary functions (for 2D cases) as well as two boundary conditions that reflects the acoustic air-material interface capability. All the FDTD methods outlined in previous paragraphs have something in common: they rely on the ZK equations to account for the drag forces on a porous material; most of them use additional constitutive, or auxiliary, equations to describe internal propagation through the material; they need multiple measurements to completely characterize the unknown parameters, highlighting that measurement protocols are very susceptible to errors due to their accuracy. In the present paper, the proposal of a Numerical Equivalent Acoustic Material (NEAM), with equivalent properties that allow an accurate simulation of material's behavior, using time domain analysis, is presented. NEAM model exchanges the effective density and the effective compressibility parameters for some phenomenological coefficients that must be adapted to achieve simulated absorption coefficient results that are equal to those measured in a Kundt tube. A similar strategy was taken into account by [PERSON] et al. [22], for the optimization of the non-acoustic parameters of a porous material, following the methods of [PERSON] [23], and [PERSON], [24]. From acoustic impedance measurements performed in a Kundt tube, and proceeding with a least squares minimization method, they were able to adjust the real and the numerical impedances and wavenumber, thus creating what the authors call an \"Artificial Porous Material\". In another work by the same authors [25], an analogous optimization procedure can be observed to obtain, in this case, the parameters of a fibrous material. The paper structure is as follows.