Open access

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Sound Field Modeling in Architectural Acoustics
using a Diffusion Equation Based Model
N. Fortin1,2, J. Picaut2, A. Billon3, V. Valeau4, A. Sakout1
1LEPTIAB (University of La Rochelle)
2ESAR (Laboratoire Central des Ponts et Chaussées)
3INTELSIG group (University of Liège)
4LEA (University of Poitiers)
The authors wish to thank
the Agence de l’Environnement et de la Maîtrise de l’Énergie (ADEME)
for providing financial support of this work.

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Introduction
Sound field modeling in room acoustics
Predicting sound level, reverberation time, acoustical parameters
for Concert Hall, dwelling, building…
Many propagation phenomena: reflection, absorption, diffusion,
transmission, scattering, diffraction…
Solutions:
Solving the wave (or Helmholtz) equation:
Analytical : no solution for “real rooms”
Numerical: finite element method limited for low frequency only
Others methods (energetic approaches, high frequency)
Statistical theory of reverberation: “simple” geometries
Ray-tracing (and similar): high computational time for “complex” rooms
Alternative solution: diffusion model
Good compromise acoustical results/computational time

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Diffusion model (1)
Diffusion model (MDF)
initially proposed by the authors for empty rooms with
diffusely reflecting boundaries
following a diffusion process (diffusion equation)
validated in many room configurations:
orectangular rooms, long rooms, coupled rooms…
oby comparison with
•others analytical models,
•numerical models (ray-tracing)
•experimental data

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Diffusion model (2)
Diffusion equation
Diffusion coefficient
tF
ttw
twD ,
,
,r
r
r
3
c
D
wacoustic energy density
room mean free path (4V/S)
csound speed

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Diffusion model (3)
Boundary condition wall
( a, )
outin
in 4w
c
wh
w
D
n
4
a c
h
hexchange coefficient
nwall normal
a wall absorption coefficient
transmission coefficient
)1ln(
4
a  c h
(Eyring’s absorption)(Sabine’s absorption)
wout win