# Binaural Auralization of Room Acoustics with a Highly Scalable Wave-Based Acoustics Simulation
## 4 Binaural Room-Acoustics Auralization in a Large-Scale Auditorium
### Analyzed Model and Computation Setting  
Figure 6 presents the auditorium model for demonstration: 2271 m\({}^{3}\) with a source point (blue sphere) and six receivers (magenta spheres). The source is located at (\(x\), \(y\), \(z\)) = (2.1, 0, 1.2) and the locations of the receivers are listed in Table 2. We calculated BRIRs, including frequency components up to 5 kHz for two acoustic treatment cases, respectively designated as Cond. 1 and Cond. 2. The first uses the following acoustic treatment as a baseline: rigidly backed glass wool absorbers of 24 kg/m\({}^{3}\) with 50 mm thickness (GW24K) were installed on the ceiling. In addition, GW-backed microperforated panels (MPPGW) were attached for the back wall, which also uses GW24K. For the audience seat area, rigidly backed needle felt (NF) with 15 mm thickness was installed. Other boundaries were treated as reflective materials having a statistical absorption coefficient of 0.175. The latter, Cond. 2, has further installed additional GW24K to side walls to suppress flutter echoes caused by multiple reflections between side walls. Other configuration details are the same as those of the baseline. The GW24K, MPPGW, and NF were modeled by the frequency-dependent impedance BCs, whereas other reflective materials were modeled by real-valued frequency-independent impedance BCs. We calculated the acoustic admittance of sound absorbers for frequency-dependent impedance BCs by the transfer matrix method [33], where the acoustical characteristics of GW24K and NF were modeled, respectively, using the Miki model [34], respectively assuming the flow resistivity of 6900 Pa s/m\({}^{2}\) and 10,000 Pa s/m\({}^{2}\). In addition, MPP was modeled with the Maa model [35], considering 0.5 mm panel thickness, 0.5 mm hole diameter, a perforation ratio of 0.55 %, and dynamic viscosity of the air of 17.9 uPa s. The resulting acoustic admittance was fitted further with a multi-pole model with \(n_{\text{rp}}=3\) and \(n_{\text{cp}}=3\) for GW24K, \(n_{\text{rp}}=2\), and \(n_{\text{cp}}=2\) for NF and \(n_{\text{rp}}=10\) and \(n_{\text{cp}}=5\) for MPP-GW. Detailed parameters of the multi-pole models are reported in the relevant literature [9]. Figure 7 presents statistical absorption coefficients for three absorbers: GW24K, MPPGW, and NF. Figure 8 also presents a comparison of average absorption coefficients of auditorium between two absorption conditions. Cond. 2 is associated with higher absorption coefficients than those of Cond. 1 at 250 Hz and higher by virtue of the additional absorption treatment on the side walls. The impulse response of an optimized FIR filter designed with the Parks-McClellan algorithm having a flat spectrum from 80 Hz to 5 kHz was used as a sound source signal. Its waveform and spectrum are presented in Figure 9. This source signal is beneficial for evaluating acoustic parameters and auralization purposes compared to a well-used Gaussian pulse having a non-flat spectrum. The auditorium model was spatially discretized by various-sized 8-node hexahedral FEs having edge lengths of less than 0.015 m. The resulting FE mesh has 742,561,152 elements and ensures spatial resolution of 4.6 elements per wavelength at 5 kHz. A theoretical estimation shows the FE mesh can keep dispersion error of less than 1% [9]. After meshing, the computational model is divided into 6144 subdomains by partitioning software Metis [28]. Regarding the reference, the coefficients of variance in DOFs and communication data among subdomains were 0.3% and 11.8%, respectively. Then, the massively parallel wave-based computation was performed with 6144 CPU cores under the same cloud computing environment as that described in Section 3 to simulate the auditorium room acoustics. Figure 8: Average absorption coefficients of the auditorium for two absorption conditions. Figure 6: Auditorium model for demonstrating binaural auralization application. Blue and magenta spheres respectively represent a source point and receiving points.