## 1 Introduction
Their preliminary study defined the threshold for the noticeable simplification of the structure size, 70 cm, i.e., there is no need for modeling details beyond this size. [PERSON], [PERSON], and [PERSON] [24] proposed an automatic geometry reduction method, which could simplify the model by reducing irrelevant small details. They concluded that, although this method could be applied in some cases, it needs to be more robust to obtain more reliable results. The LOD in a GA model affects the generated sound field, which is strongly related to the presence and typology of diffusive surfaces; thus, their acoustical characterization becomes crucial [25; 26; 27]. However, general rules are still used to assign the diffusive properties in simulated environments [20; 28; 29]. As reported in [PERSON] and [PERSON] [30], very different scattering coefficient values could produce very different sound fields. They found that models with lower LOD do appear to have greater sensitivity to the scattering coefficient selection, but the changes that have been observed in the parameters did not occur in a consistent manner across all of the halls studied [31]. [PERSON] and [PERSON] [30] showed that the scattering coefficient variations do not affect the results of clarity (\(C_{80}\)) and lateral fraction (\(LF_{80}\)). The most affected parameters are early decay time (\(EDT\)) and reverberation time (\(T_{30}\)), which exceeded more than two JND-s (Just Noticeable Differences) from the reference model. [PERSON] [20] showed through simulations with different scattering algorithms that the most affected parameter from the scattering coefficient changes was \(T_{30}\). [PERSON], [PERSON], and [PERSON] [32] found that the diffusive surfaces applied on the areas of the proscenium splay help to keep stage-to-pit ratios of interaural cross-correlation (\(IACC\)) high, but, on the other hand, distribute the energy to many reflections over time rather than concentrating it in strong early reflections, leading to decreases in \(C_{80}\). Another variable, which is shown to be influential in determining the model's sensitivity to scattering coefficient, is the listener position [16; 30]. A receiver closer to the wall is more sensitive to changes in scattering coefficients than a receiver far from the wall. This sensitivity is particularly related to changes in \(T_{30}\). The contribution of all these variables makes it more challenging to draw a general analytical formula that could relate the scattering coefficient to the acoustic parameters [33]. The correct evaluation of these parameters must also consider the scattering variable, since the realistic environments do not have a perfect diffuse field [34]. Based on these studies, it is evident that the accurate physical simulation of room acoustics is a very complex task. The decision of how much precision should be required from the prediction models relies on our ability to detect differences between reality and simulations. The auditory system seems to be insensitive to many aspects, e.g., small variations in the surface scattering properties [35]. Therefore, the prediction of room acoustical perception needs to take the insensitivity of the auditory system into account. This is linked to the JND of the acoustic objective and subjective parameters, which allows for the characterization of a space and enables numerical comparison between different environments. The simulation using numerical techniques gives clues as to how a performance hall would sound when achieved. Thus, it becomes crucial for the investigation of different alternatives and for the control of the design costs. Acousticians, performers, and architects agree on the need for well-defined objective descriptors that would allow for quantifying specific subjective impressions of the acoustics of the performance space. Especially in enclosed spaces, humans are quite sensitive to the perception of sound in all its temporal, spectral, and spatial aspects, which makes a realistic auralization in room acoustics quite challenging.