PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Preliminary results of scattering surface modeling and perceptualaspects in wave-based acoustic simulations
Louena SHTREPI1; Brian HAMILTON2; Arianna ASTOLFI1; Marco MASOERO1
12

Politecnico di Torino, Italy

University of Edinburgh, UK

ABSTRACTThe level of detail of a simulated model as well as the assignment of the materials acoustic properties havebeen largely debated and optimal guidelines have been determined based on the approximations of thescattering algorithm of the simulation tools. These aspects are of great importance when investigating thedifferences between geometrical-acoustic (GA) based and wave-based methods. To this aim the present study
refers to objective and subjective evaluations of wave-based simulations (finite difference time domain
method) in a shoebox concert hall, which has been previously studied through GA-based methods. Threemodels, that consider 1) reflective, 2) low scattering, and 3) high scattering conditions of one of the longlateral walls, have been simulated in order to determine the conventional acoustic parameters such as early
decay time (EDT), reverberation time (T30), clarity (C80), definition (D50). GA-based and wave-based
simulation results have been compared to measured data. Furthermore, a preliminary subjective investigation
has been performed in order to determine the sensitivity of listeners to the surface diffusivity variations indifferent listening positions.
Keywords: Sound, Simulation, Wave-based, Scattering, Level of modeling detail.

1. INTRODUCTION
The level of modeling detail (LOD) has been object of continuous research since the geometricalacoustic (GA) models have been introduced as a predictive tool (1–3). More in depth has been
investigated objectively and subjectively also the diffusive surface modeling detail (4,5). The basis of
this interest is mainly related to the fact that the LOD is considered a systematic uncertainty factor in
GA models. Conversely, it should be considered that a high level of detail leads to an increase of theGA modeling efforts, which can be time consuming. The LOD related to diffusive surface modeling isalso of interest for finite-difference time-domain (FDTD) simulations (6,7) approximating the wave
equation in the context of room acoustics. However, more insight is needed regarding the LOD issues
in FDTD simulations (8).
Besides the objective parameters that might be affected at some extent by the LOD , also theauralizations plausibility must be considered. It is very important to simulate in an appropriate way thetemporal, spectral, and spatial aspects of an impulse response, which are strongly affected by thepresence of diffusive surfaces (9).
In this study, the FDTD method (10) has been used to simulate the model of a variable-acoustics
concert hall. The work consists of the simulation of two conditions of one lateral wall, which are put ina reflective and diffusive configuration. The aim of the simulations is to examine the effect of surface
structures on the reflected sound through comparisons with measurements and GA-based simulations
based on ISO 3382 acoustic objective parameters: early decay time (EDT), reverberation time (T30),
clarity (C80), and definition (D50).

125990louena.shtrepi@polito.it
brian.hamilton@ed.ac.uk

2. METHODS2.1 Room model
The model of a shoebox concert hall, the Espace de Projection at IRCAM in Paris (Figure 1), hasbeen considered in these simulations. This room has been extensively studied both throughmeasurements (11) and simulations (4) based on GA software (Odeon 13.00); thereby in this work
have been introduced only the conditions of its simulation with an FDTD method.
The room has a rectangular geometry (24 m × 15.5 m × 10 m) and a variable acoustics. Thegeometry and the acoustical properties of the hall can be varied by controlling 172 independently
rotating prismatic module panels (2.3 × 2.3 m). The variable acoustics is obtained by varying theproperties of these three-dimensional structures; the prisms show different acoustic properties for eachface when rotated. The particularity of the room relies also on the properties of the absorptive material
which is of two typologies: absorptive at low frequencies (type A), while the other one absorbs at highfrequencies (type B).
Two conditions were considered in the framework of this study. The two hall configurations, whichhave been considered also in (4) and (11) were chosen. The models are generated by varying theproperties of only one lateral wall and maintain the same conditions of the rest of the room. The lateralwall was set at two different acoustic conditions: reflective and diffusive. The ceiling and the otherwalls have been fixed to an absorptive condition with absorption coefficients based on type A and type
B panels’ properties. The floor has been considered as a hard-reflective surface. Two separate CAD
models have been created (Figure 1, a and b): the reflective condition (RF), which is modeled with flat
surfaces, and the diffusive condition, which has diffusive surfaces modeled as 3D triangular structure(DM). Material properties are expressed in terms of acoustic admittances assigned as boundary
conditions to surfaces (10).

a)

b)

c)

d)

Figure 1 – Snapshots of wave propagation in FDTD model confined to x-y plane at with point source at 3.7m
height, in calibration model (DM, left) and reflective model (RF, right). Diffraction due to variations inmaterial at left wall is clearly visible (c and d). Scattering due to diffusive geometry can also be observed.

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2.2 Numerical method
The numerical method used for the wave-based simulations is the FDTD method described in (10).
The numerical grid spacing for these FDTD simulations were chosen such that approximation errors in
the form of numerical phase velocity were below 2% up to 8kHz. As the FDTD method solves the wave
equation directly, diffraction and scattering are inherently simulated by waves interacting with themodel geometry (see, e.g., Figure 1).
2.3 Calibration
Despite a high level of fidelity to the physical acoustics afforded by the FDTD method, somecalibration of the model can be expected due to input data uncertainties. Additionally, boundaryconditions for the employed FDTD method are generally specified in terms of complex impedances(modelling frequency-dependent absorption), but complex impedance data were not readily available.
As such, diffuse-field absorption coefficients were used as a starting point to find a complex
impedance with a target absorption profile (see, e.g., (10)). The absorption coefficients calibrated fromthe GA simulations in (4) were used as a starting point for calibrating the FDTD method. Focusing
primarily on the diffusive surfaces, absorption coefficients were calibrated according to measured
T30s following general guidelines established for the calibration of GA models (4, 12). T30s obtained
from simulated data were found to be within approximately one JND with respect to measurements(Figure 2). It can be observed that also the other parameters show a good match with the measured date,
except for the frequency 125 Hz. In this instance, this agreement was achieved by varying absorption
coefficients within +/- 0.04 Sabins/m2 of values provided in (4).

Figure 2 –Objective acoustical parameters for calibration model (DM1) obtained after initial calibration.
2.4 Simulation set-up
The simulation set-up consisted of 24 receivers and one source position. The receivers covered one
half of the room and have been located at a height of around 3.70 m from the floor level. The soundsource also was maintained unvaried and positioned midway between the axis of symmetry of theroom and the lateral wall. The post-processing of the simulated data has been carried out using
ITA-Toolbox, an open source toolbox for Matlab (13).
2.5 Room acoustic parameters
The same parameters used in GA simulations and measurements analyses based on of ISO 3382 -1(14) have been used also for the FDTD simulations. The values of four parameters, that is,reverberation time (T30), early decay time (EDT), clarity (C80), definition (D50), have been presented
in octave bands as mean values over all the receiver positions in order to assess the accuracy of the5992

calibration process. ITA-Toolbox, which comply with the ISO 3382-1:2009, has been used to analyze
the impulse responses. The Just-Noticeable Differences (JNDs) has been used as criteria to judge thesignificance of the variations due to the change of the surface properties.

3. PRELIMINARY RESULTS AND DISCUSSIONSThe FDTD method has been used in this study to investigate the differences between the reflective(RF) and diffusive (DM) condition of a lateral wall in a shoebox concert hall. First a calibration
process has been shown and the objective acoustic parameters based on ISO3382 have been estimatedand compared to measured and GA-based simulations results. Acoustic properties assigned within theFDTD method were adjusted with respect to the GA simulations in order to calibrate to measurements.
The objective evaluation of T30, EDT, C80, and D50 in each model (RF and DM) showed a good
match with the measured data. The calibrated simulation results will serve as the basis of listening tests
to evaluate perceptual accuracy. A perceptual evaluation will be carried out through listening tests inorder to determine the difference between the reflective and diffusive condition. All the objective andsubjective results will be compared to the in-field measurement and Odeon (v13.00) simulation results,
that have been introduced in (4, 11).
The findings of this study aim at giving more insight on the fidelity of FDTD simulations of concert
halls and large spaces, and at establishing guidelines for calibration processes in the presence of
uncertain input data.

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