Treble simulation of diffraction (RS5)
Treble simulation of diffraction (RS5)
Diffraction is a prominent low frequency phenomenon that is known to be difficult to simulate with traditional geometrical acoustics (GA) software even with some compensations. Treble outperforms the conventional GA software in simulating diffraction by directly solving the wave equation. In this study we compare Treble simulations with measurements included in BRAS (Benchmark for Room Acoustical Simulation) RS5 scene. There is a very good agreement, showing that solving the wave equation is the best way to simulate sound fields with strong diffraction.
When there is an impenetrable obstacle between a sound source and a receiver, sound diffracts around the obstacle. Examples include diffraction around a noise barrier outdoors and diffraction through open doors that enables to hear others who talks in adjacent rooms even though they are not visible from the receiver. Diffraction is an important phenomenon in room acoustics that traditional energy-based geometrical acoustics methods struggle to simulate. There are some ways to add diffraction in geometrical acoustics, such geometrical theory of diffraction  and analytical secondary source modeling  etc. Treble’s wave-based solver, discontinuous Galerkin method, solves the wave equation directly, so the Treble’s solution must be superior to the energy-based geometrical method. In this work, a diffraction scenario is simulated in Treble, which is RS5 case e in BRAS database , as shown in Fig. 1.
Figure 1. Diffraction measurement setup, RS5 in BRAS .
A Genelec 8020C sound source was used and an omni directional microphones GRAS 40A was used in the hemi anechoic chamber RWTH Aachen (V = 296 m3) with a low frequency cutoff of 100 Hz. The MDF panel has a thickness of 25 mm with a height of 2.07 m. One the day of measurement, the temperature was 20.3 °C and the humidity was 40.3 %. For the RIRs, the measurement points are shown in Fig. 2. In Treble, the loudspeaker and receiver at the bottom are excluded.
In Treble, the simulation was done up to 2000 Hz (as transition frequency) only by the wave-based solver. Due to the dispersion error at higher frequencies, the simulations and measurements are compared up to 1800 Hz. The source is modeled as omni source, as the diffraction is prevailing at low frequencies where the loudspeaker typically radiates omni-directionally. The impulse response length is set to 25 ms.
Figure 2. Source and receiver locations for RIR measurements (left) and Treble screen shot (right).
For the LS02 and MP01 (without any line of sight), Treble and Raven simulations are compared to the measurement in Fig. 3. It is clear that Treble shows a better agreement in the trough locations, which actually shows destructive interference due to diffracted wave components from the edges. The state-of-the-art geometrical acoustics that can take diffraction into account cannot simulate this diffraction case as accurately as Treble.
Figure 3. Comparison between simulation and measurement.
In Figs. 4-6, the transfer functions at three sources and three receiver locations are compared between measurements and Treble simulations. In all cases, there are good agreements observed.
Figure 4. Comparison between Treble and measurement for LS2.
Figure 5. Comparison between Treble and measurement for LS3.
Figure 6. Comparison between Treble and measurement for LS1.
This study investigates how sound diffracts around a large plate in Treble simulation, which is experimentally validated against BRAS RS5 data. It is clear that treble simulation outperforms the other state of the art geometrical acoustics simulation because it directly solves the wave equation. The main sources of errors are uncertainties in the source and receiver locations, an omni-directional source modeling in Treble, and spurious reflection possibly from the room surfaces in Treble as the random incidence absorption coefficients of the boundary walls are 95%, not fully absorptive. Despite all the uncertainties, the Treble simulation is convincing, which is a strong point for simulating room acoustics at low frequencies.
 JB Keller, “Geometrical theory of diffraction,” Journal of the Optical Society of America, 52 (2), 116-130 (1962).
 UP Svensson, RI Fred, J Vanderkooy, “An analytic secondary source model of edge diffraction impulse responses,” Journal of the Acoustical Society of America 106 (5), 2331-2344 (1999).
 Benchmark of Room Acoustical Simulation (BRAS) database RS5: https://depositonce.tu-berlin.de/bitstreams/ccce535a-c508-4046-8748-4458b8e73d13/download