PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Numerical simulation of in-vehicle sound field under conditions ofopen or closed car windows
Linda Liang†1,2, Guangzheng Yu*1,2, Le Yu1
1

School of Physics and Optoelectronics, South China University of Technology, Guangzhou, China
2

School of Architecture, South China University of Technology, Guangzhou, China

ABSTRACTAs computation technology develops, sound field numerical simulation in-vehicle has attracted more andmore attention. However, it is difficult to simulate sound field in-vehicle at high frequency by using
wave-equation-based numerical methods, such as finite element method (FEM), finite difference in time
domain (FDTD), etc. To extend the region of effective frequencies, a combined method consisting of finite
element method (FEM) and ray-tracking method can be used to simulate the sound field in a car. Even so, thecombination of the spectrum at the segmentation frequency between two methods still remains a well-known
problem and is worthy of investigating. In this work, only the improved FEM was adopted to simulate thein-vehicle sound field. Through an optimized car model with smoothing fine structures and non-uniform
meshing grids, the computation was optimized and the effective frequency was extended up to 4 kHz. Further,sound field distributions under conditions of open or closed lateral front windows (the condition of open
windows is approximated by an absorptive boundary) were simulated and analyzed, so as to validate theoptimized car calculation model and numerical method.
Keywords: Finite element method, Sound field in-vehicle, Numerical simulation

1. INTRODUCTION
Automotive environment is increasingly becoming an indispensab le listening space in our daily
life. There are two components of the acoustic environment in the automobile cabin: the noise due toautomotive processes or surroundings and the sound field effect produced by the car audio system (1).
The acoustic environment in an automobile cabin has a significant effect on the perceived soundquality of the vehicle. In fact, because of the particularity of in -vehicle sound field compared withtraditional room sound field, which is caused by a small-size space (2), the research on the sound fieldin-vehicle still remain to be further developed.
In order to design and predict a better sound reproduction performance inside the car, numericalsimulation is a common, low-cost and high-efficiency technical approach. The general numericalsimulation methods include ray-traking (RA) (3), finite difference in time domain (FDTD) (4),boundary element method (BEM) (5) and finite element method (FEM) (6). In theory, geometricalacoustics can only be used at frequencies where the wavelength of the sound is considerably smaller
than any structure scale in the target acoustic space (7). When the size of reflecting objects becomecomparable to the wavelength of sound, a wave-based method is predominant. The FEM is attractive
because of its inherent accuracy and its ability to handle arbitrary model shape compared with BEM,
but it is limited to low frequencies and small rooms due to large computation amount (requiring morememory and computation time) and higher requirements for the finer structures. Therefore, it isnecessary to optimize FEM, so that it can be used to simulate the sound field in -vehicle up to higher
frequencies.
Actually, FEM has being developed in recent years (8-11). To extend the region of effective
frequencies, Aretz used a combined method consisting of finite element method (FEM) andray-tracking method to simulate the sound field in a car up to 12 kHz, in which the segmentation
frequency is approximately 800 Hz (12). Even so, the combination of the spectrum at the segmentation
frequency between two methods still remains a well-known problem and is worthy of further†1015307923@qq.com*

Corresponding author: scgzyu@scut.edu.cn

4364

investigation. In particular, in the context of the rapid development of computer technology, moreaccurate simulation under shorter computing time can be obtained and thereby guiding the design ofsound reproduction.
As mentioned previously, there is a contradiction between improving calculation accuracy (suchas extend effective simulation to higher frequencies) and the computation volume (or time cost).
There, first, we propose an optimized car model with smoothing fine structures and non-uniform
meshing grids, the use of eight-noded cubic volumic element, the computation was optimized and theeffective frequency was extended up to 4 kHz, which covers the frequency range of speech. Many
factors can contribute to a vehicle’s interior sound field. For sound reproduction inside the car, theearly reflections caused by the lateral front windows seems to play an important role, owing to theirclose distance from the ear (13). Therefore, the influence of the lateral front windows on the soundfield inside the car was predicted by using the optimized FEM in time domain, which also validate theoptimized method. Sound field distribution under two different acoustic boundary conditions, which
simulates the lateral front windows being close or open. This work will play an important role inauralization researches in-vehicle.

2. Calculation model
2.1 Mathematical Model
The simulation work in this paper was carried out using the acoustics model in the COMSOLMultiphysics software. The stimulus signal used in this model is time-harmonic, on which the soundpropagation in the car cavity can be described by the inhomogeneous Helmholtz equation:

1
ρc
pt

2



w 2 ptwt2·§ 1
   ¨¨ pt  q d ¸¸
¹
© ρ

Qm

,

(1)

p  pbwhere ρ is the fluid density (SI unit: kg/m3), c refers to the speed of sound in medium (SI unit: m/s), pt
indicates to the total sound pressure (SI unit: Pa), Qm denotes as the monopole domain source(SI unit: 1/s2),
qd is the dipole domain source (SI unit: N/m3), p is the sound pressure (SI unit: Pa), and pb is the pressureof background sound field (SI unit: Pa).
In the finite element domain, the impedance boundary approach ignores possible fluid-structural
coupling effects caused by vibration of the car materials. It is assumed that the sound wave propagates
only from the direction of the vertical surface. Therefore, the impedance is not affected by the incident
sound field, thus can be represented by a constant. Absorption boundary condition can be described byfollowing equation:

§ 1
·
1 wpt
 n  ¨¨ pt  q d ¸¸
Z i wt© ρ¹where Z i is the characteristic acoustic impedance (SI unit: Pa·s/m).

(2)

2.2 geometric model
Finite element analysis is a general analysis tool. It is commonly possible to import geometricmodel data from CAD files. Figure 1 shows the model used in this simulation, which is a simplified
model based on the actual size of a real car.The model consists of an enclosed cavity and simplified
seat, a point source, s 1, and a receiver point, r 1.
For the purpose of improving the calculation efficiency and ensuring the accuracy, the eight-noded
cubic volumic element is used in the calculation (14). In order to ensure the accuracy of the calculation
model, the maximum size of the meshing unit should be less than one -sixth of the wavelength.
Moreover, for the interior surface of the car with a mutated shape, the mesh near it was refined, and thegrid cell size was slightly larger for the continuum in the car cavity. In this way, the interior of the car
was divided into many non-uniform grids. Finally, the total number of grid cells is 202117, the largest
element size is 0.0274 m, and the minimum element size is 0.00504 m. Such grid cell settings are morethan sufficient for calculating the sound field in the time domain within the 4 kHz frequency range.

4365

Figure 1-Model of the car cabin and diagram representing x-y (blue) and y-z (green) cross section
2.3 Source and boundary condition
When calculating the impulse response in a car, it is necessary to add an stimulus source for the
calculation. In actual measurement, the maximum length sequence (MLS) or the sweep frequency signal isusually used as the excitation sound source to reduce the influence of noise on the measurement result.
However, in numerical simulation, because there is no influence of environmental noise, the pulse soundsource can be selected as the excitation signal, which makes the calculation simulation more efficient.
Gaussian pulses are commonly used signals in time domain simulation. In this paper, Gaussian pulse isused as the excitation sound source for simulation. The time domain expression was as follows:22­
 π 2 f0 t  t p
Q
e
$
°
° m
,
(3)
®
1
1
°t p 
 t  tp 
°
f0
f0
¯
where A is the amplitude (SI unit: m2/s), f0 is the frequency bandwidth (SI unit: Hz), and tp is the durationof the pulse (SI unit: s), respectively.
Taking into account the computational time that could be limited by computer hardware, the time step∆t was set as 0.125 ms, and the corresponding sampling frequency 1/∆t was 8 kHz. According to thesampling law (15), the effective frequency that can be accurately calculated under such sampling frequency
setting is 4 kHz. The impulse response of the four receiving points can be directly calculated.
When the lateral front windows were close, the impedance boundary conditions of the side windows
and the front-rear windscreen were set to 8712 Pa∙m/s. However, it is worth mentioning that we replaced
the impedance of the front side windows with the impedance of the air, 439.89 Pa∙m/s, to simulate theboundary condition of lateral front windows that were open, as shown in Table 1. In addition, theimpedance conditions of seats and other panels were set as 8852 Pa∙m/s, and 3142 Pa∙m/s, respectively. The
point source and the receiver point located at coordinate (2.4 m, 1.4 m, 1 m) and (2.4 m, 2.2 m, 1 m),
respectively, as shown in Figure 1. The heights of the point source and the receiver point are close to theheight of the human head when a person is sitting in the car.
Table 1 – The impedance setting of surfaces inside car under two conditions
Front-rear Rear side
Right front
left front sideseatothers
Impedance (Pa·m/s)
windscreen windows side window
window
lateral front windows closed 8852
8712
8712
8712
8712
3142
lateral front windows open

8852

8712

8712

439.89439.893142

3. Results and Analysis
The FEM can obtain the numerical solution of each element in the solution domain. In order topredict the effect of the window compartment on the sound field distribution, t he sound field

4366

distribution in both x-y, y-z cross sections (see Figure 1) along the source point in the coordinate
system have been obtained. Then, the sound propagation in cross section in the time-domain under
different conditions have been observed, which are shown in Figure 2 and Figure 3, respectively. All
these figures illustrate the time domain propagation of sound wave from 0.5 ms to 4.5 ms with 0.5 ms
interval.

Figure 2- The propagation procedure of sound field on x-y cross section inside car with lateral front
windows open (left) and closed (right), where dotted line frames represent open windows while solidline frames represent closed windows

Figure 3-The propagation procedure of sound field on y-z cross section inside car with lateral front
windows open (left) and closed (right), where dotted line frames represent open windows while solidline frames represent closed windows
Figure 2 shows the time-domain propagation procedure of sound wave on x-y cross section alongsource position in car cabin, under the conditions of open and closed lateral front windows. We can see
that, will interfere with the direct sound and contribute to the resulting sound field. Due to the small
size of car, sound wave can travel to the interface within several millisecond. Therefore, the soundpropagation is more strongly influenced by these wave effects. When the lateral front windows areclosed, we found that the reflection of the front window smears the time signature of the sound field in
the car cabin, just like Figure 2 (right) when the propagation time is more than 2.0 ms.
Similarly, Figure 3 illustrates the time domain diagram of sound wave propagation. When soundpropagates to the open window, a significant sound energy leakage can be observed in the figure.
Comparing the two groups of time domain propagation figures, when the lateral front windows areclosed, that is, when the lateral front window was set as the absorptive boundary, the sound field
focusing seems to appear more frequently.
Figure 4 shows the impulse response at receiver point r 1 (in driver seat) under different boundary
conditions, namely closed and open lateral front windows. The sound field inside vehicle consists

4367

entirely of direct sound and early reflections, which are quickly absorbed or dissipated (the shortduration within about 20-30 ms). This is due to the small dimensions of the vehicle interior, namely
the emitter is close to reflection/absorption boundary. However, it is difficult to discover the obvious
difference between the two impulse responses.

Figure 4- The impulse response in receiver point r1 with lateral front windows closed
open (red) and their waveform comparison(blue),

Table 2-The magnitude spectrum statistics in octave of two impulse response at receiver point r1
Frequency (Hz)

31.5

63

125

250

500

1000

2000

Magnitude withlateral front windows
close-24.0 dB

-28.2 dB

-19.8 dB

-18.0 dB

-16.9 dB

-5.3 dB

0 dB

Magnitude withlateral front windows
open-29.0 dB

-32.3 dB

-21.2 dB

-18.5 dB

-17.5 dB

-6.9 dB

0 dB

The magnitudedifference

5.0 dB

4.1 dB

1.4 dB

0.5 dB

1.0 dB

1.6 dB

0 dB

Further, the magnitude spectrum statistics in octave of the two impulse responses can be got withdirac software, as shown in the Table 2. it can be found that the magnitude of the spectral intensity
under the condition of lateral front windows open is generally lower than that of windows close , due
to the sound energy leakage. Moreover, it’s worth noting that there is more significant difference in
low frequencies, which indicates that the sound energy leakage mainly occurs in low frequencies.
For a typical vehicle, the decay time for a 60 dB signal reduction is 30 to 50 ms. Therefore,
reverberant field cannot form in the environment of this size, whose reverberat ion time istremendously small. This reason could be that the sound path between two reflectors is short, that issay, the sound wave can frequently reach the absorptive boundaries, and thus the sound the energy isquickly absorbed by the sound absorptive boundary. Because the absorption interface absorbs morehigh-frequency sound, the sound wave in the car attenuates faster at high frequency, so that thereflection times are less when the sound wave propagates in the car. On the other hand, the frequencyof low-frequency reflection is more, so after the low-frequency energy leakage caused by window
opening, the energy statistics will be less.

4. CONCLUSIONSThis work aims to design a finite element model with simplified car interior, which is applied tohigh frequency in order to investigate how sound propagate inside car cabin with the influence oflateral front windows. Through an optimized car model that combines the used of eight-node cubic
volumic element, smoothing fine structures and non-uniform meshing grids, the calculating procedure4368

was optimized and the effective calculation frequency was extended up to 4 kHz, which covers thefrequency range of speech. The influence of the lateral front windows on the sound field distribution
inside the car has been analyzed. We obtained the time domain variation figures of the sound field
propagation on different cross sections of the vehicle with the setting of the Gaussian pulse pointsound source. Results show that, in general, most of the energy of sound field inside the car isconcentrated in direct sound and early reflection. Sound waves can be attenuated quickly in the car,which can be attributed to the smaller size of the car. The closing or opening of the window has asignificant effect on the reflection and absorption of sound waves in the vehicle. Incontestable, theopening and closing of the window has a great influence in the distribution of the sound field in the car,which is manifested in the more frequent sound focusing when the windows are closed and the greater
influence of the low-frequency energy attenuation when the windows are opened. It can be found thatthe setting of the side window is indispensable when we study the sound field in the car.

ACKNOWLEDGEMENTS
This work was supported by the National Natural Science Foundation of China (Grant No.
11574090) and the Natural Science Foundation of Guangdong Province (Grant No. 2018B030311025).

REFERENCES
1. Cheer J. Active control of the acoustic environment in an automobile cabin (Doctoral dissertation,
University of Southampton, 2012).
2. Strauss M, Nowak J, de Vries D. Approach to sound field analysis and simulation inside a car cabin. In
Audio Engineering Society Conference: 36th International Conference: Automotive Audio 2009 Jun 1.
Audio Engineering Society.
3. Jeong CH, Ih JG, Rindel JH. An approximate treatment of reflection coefficient in the phased beam
tracing method for the simulation of enclosed sound fields at medium frequencies. Applied Acoustics.
2008 Jul 1;69(7):601-13.
4. Celestinos A, Olsen M, Møller MB, Lydolf M. Car interior simulation model for low frequencies using
the finite difference time domain method. In Audio Engineering Society Conference: 48th International
Conference: Automotive Audio 2012 Sep 21. Audio Engineering Society.
5. M. Behzad, M. Hodaei, I. Alimohammadi, Experimental and numerical investigation of the effect of aspeed bump on car noise emission level, Applied Acoustics, Volume 68, Issues 11–12,2007, Pages
1346-1356.
6. Hu L, Shi Y, Yang Q, Song G. Sound reduction at a target point inside an enclosed cavity using particle
dampers. Journal of Sound and Vibration. 2016 Dec 8; 384:45-55.
7. Granier E, Kleiner M, Dalenbäck BI, Svensson P. Experimental auralization of car audio installations.
Journal of the Audio Engineering Society. 1996 Oct 1;44(10):835-49.
8. Xu Z, Xia X, Lai S, He Z. Improvement of interior sound quality for passenger car based on
optimization of sound pressure distribution in low frequency. Applied Acoustics. 2018 Jan 15;
130:43-51.
9. Zaleski O, Keuchel S, Von Estorff O. Numerical Design of Loudspeaker Systems in a Car Cabin. SAE
Technical Paper; 2018 Jun 13.
10. Yamade Y, Kato C, Yoshimura S, Iida A, Iida K, Onda K, Hashizume Y, Gou Y. Prediction of
aeroacoustical interior noise of a car, part-1 prediction of pressure fluctuations on external surfaces of acar. SAE Technical Paper; 2016 Apr 5.
11. Iida K, Onda K, Iida A, Kato C, Yoshimura S, Yamade Y, Hashizume Y, Guo Y. Prediction of
Aeroacoustical Interior Noise of a Car, Part-2 Structural and Acoustical Analyses. SAE Technical Paper;2016 Apr 5.
12. Aretz M, Vorländer M. Combined wave and ray-based room acoustic simulations of audio systems in
car passenger compartments, Part I: Boundary and source data. Applied acoustics. 2014 Feb 1;
76:82-99.
13. Soeta Y, Sakamoto Y. An Exploratory Analysis of Sound Field Characteristics using the Impulse
Response in a Car Cabin. Environments. 2018 Apr;5(4):44.
14. MacNeal RH, Harder RL. A refined four-noded membrane element with rotational degrees of freedom.
Computers & Structures. 1988 Jan 1;28(1):75-84.
15. Xie B. Head-related transfer function and virtual auditory display. J. Ross Publishing; 2013 Jul 23

4369