Computational Simulation in Architectural and Environmental Acoustics: Methods and Applications of Wave-Based Computation

332 Pages·2014·18.7 MB·English

by  Tetsuya Sakuma

Tetsuya Sakuma · Shinichi Sakamoto
Toru Otsuru E ditors
Computational
Simulation in
Architectural and
Environmental
Acoustics
Methods and Applications of
Wave-Based Computation
Computational Simulation in Architectural
and Environmental Acoustics
Tetsuya Sakuma Shinichi Sakamoto
•
Toru Otsuru
Editors
Computational Simulation
in Architectural and
Environmental Acoustics
Methods and Applications of Wave-Based
Computation
123
Editors
Tetsuya Sakuma Toru Otsuru
ShinichiSakamoto OitaUniversity
The Universityof Tokyo Oita
Tokyo Japan
Japan
ISBN 978-4-431-54453-1 ISBN 978-4-431-54454-8 (eBook)
DOI 10.1007/978-4-431-54454-8
Springer TokyoHeidelberg New YorkDordrecht London
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(cid:2)SpringerJapan2014
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Preface
With the consistent progress of computer technology, computational acoustic
simulationisnowbecomingapopular,indispensable,andpowerfultoolforsound
environmental design of architectural and urban spaces. Indeed, there are high
expectationsforawidevarietyofapplicationsforpredictionofroomacousticsand
noise propagation, development of building materials/components and audio
equipment,andvisualizationandauralizationofsoundenvironment,amongother
effects.Inthefirstdecadeofthiscentury,remarkableadvanceshavebeenmadein
wave-based acoustic simulation techniques, which are steadily increasing their
practicality and applicability.
In the meantime, the Subcommittee of Computational Acoustics on Built
EnvironmentoftheArchitecturalInstituteofJapanproposedabookinJapaneseto
review a variety of numerical methods for wave-based acoustic simulation and
recent applications to architectural and environmental acoustics, and it was
published by the institute in 2011. Following the original concept and enriching
the contents, this present book was composed in English for international publi-
cation by the editorial board and new authors were added.
Thisbookhastwomainparts,followinganintroductionprovidinganoverview
of computational simulation of sound environment. Part I explains the funda-
mentals and advanced techniques for three popular methods, namely, the finite-
difference time-domain method, the finite element method, and the boundary
elementmethod,aswellasalternativetime-domainmethods.PartIIdemonstrates
various applications to room acoustics simulation, noise propagation simulation,
and acoustic property simulation for building components, and auralization.
All authors willingly contributed the latest fruits of their own research, which
led to the successful completion of this edition. The editors have tried to make
terminology and mathematical notation consistent to some extent; however, we
begthereaders’pardonifincompletedescriptionsremain.Wehopethatthisbook
will be helpful to researchers, engineers, and students in deepening their interests
and knowledge of computational acoustic simulation.
v
vi Preface
The editorssincerely thank Dr. Yuko Sumino of Springer Japan for her advice
and assistance, and we are grateful to all authors for their cooperation. As a final
word,wedeeplyregretthatoneoftheauthors,Dr.TomonaoOkubo,passedaway
during the pre-publication editorial process. This book is one of his posthumous
works and also serves as our tribute to the memory of a distinguished acoustician
and great friend.
Tokyo, March 2014 Tetsuya Sakuma
Shinichi Sakamoto
Toru Otsuru
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Tetsuya Sakuma and Toru Otsuru
1.1 Computational Simulation for Sound Environment Design. . . . . 1
1.2 Progress of Computational Acoustics. . . . . . . . . . . . . . . . . . . . 3
1.2.1 Advent of Wave-Based Acoustic Analysis. . . . . . . . . . . 3
1.2.2 Features of Numerical Methods . . . . . . . . . . . . . . . . . . 4
1.2.3 Application to Sound Environmental Simulation. . . . . . . 5
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Part I Methods of Wave-Based Acoustic Simulation
2 Finite-Difference Time-Domain Method . . . . . . . . . . . . . . . . . . . . 11
Shinichi Sakamoto, Hideo Tsuru, Masahiro Toyoda
and Takumi Asakura
2.1 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1.1 Basic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1.2 Boundary Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.3 FDTD(2, 4) Method . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.4 Stability and Dispersion Error . . . . . . . . . . . . . . . . . . . 18
2.1.5 Absorbing Boundary Condition. . . . . . . . . . . . . . . . . . . 20
2.2 Techniques for High Accuracy . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2.1 Compact Finite Difference. . . . . . . . . . . . . . . . . . . . . . 25
2.2.2 Improvement of Time Integration. . . . . . . . . . . . . . . . . 32
2.3 Application to Vibroacoustic Problems. . . . . . . . . . . . . . . . . . . 33
2.3.1 Solid Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.3.2 Plate Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3 Finite Element Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Toru Otsuru, Takeshi Okuzono, Noriko Okamoto and Yusuke Naka
3.1 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.1.1 Sound Field Formulation by FEM. . . . . . . . . . . . . . . . . 54
3.1.2 3-D Acoustic Elements . . . . . . . . . . . . . . . . . . . . . . . . 57
vii
viii Contents
3.2 Efficient Computation with Iterative Solvers. . . . . . . . . . . . . . . 61
3.2.1 Linear System of Equations and Solvers . . . . . . . . . . . . 61
3.2.2 Estimation of Required Memory. . . . . . . . . . . . . . . . . . 64
3.2.3 Convergence of Iterative Methods. . . . . . . . . . . . . . . . . 65
3.3 Application to Exterior Problems. . . . . . . . . . . . . . . . . . . . . . . 69
3.3.1 Approaches to Exterior Problems . . . . . . . . . . . . . . . . . 70
3.3.2 Dirichlet-to-Neumann Method . . . . . . . . . . . . . . . . . . . 70
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4 Boundary Element Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Yosuke Yasuda and Tetsuya Sakuma
4.1 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.1.1 Frequency Domain BEM. . . . . . . . . . . . . . . . . . . . . . . 80
4.1.2 Time Domain BEM. . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.2 Indirect Method and Domain Decomposition Method . . . . . . . . 92
4.2.1 Indirect BEM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.2.2 Domain Decomposition Method . . . . . . . . . . . . . . . . . . 96
4.3 Application of Fast Multipole Method . . . . . . . . . . . . . . . . . . . 100
4.3.1 Application of Iterative Method to BEM . . . . . . . . . . . . 100
4.3.2 Fast Multipole Method . . . . . . . . . . . . . . . . . . . . . . . . 101
4.3.3 Fast Calculation of Matrix-Vector Products . . . . . . . . . . 105
4.3.4 Implementation Considerations. . . . . . . . . . . . . . . . . . . 110
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5 Alternative Time-Domain Methods. . . . . . . . . . . . . . . . . . . . . . . . 117
Takuya Oshima, Takashi Ishizuka and Kan Okubo
5.1 Linearized Euler Equation Method . . . . . . . . . . . . . . . . . . . . . 118
5.1.1 Governing Equations. . . . . . . . . . . . . . . . . . . . . . . . . . 118
5.1.2 Discretization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
5.1.3 Computational Setup. . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.1.4 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.2 Constrained Interpolation Profile Method. . . . . . . . . . . . . . . . . 122
5.2.1 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.2.2 Implementation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
5.2.3 Boundary Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . 129
5.2.4 Perfectly Matched Layer . . . . . . . . . . . . . . . . . . . . . . . 130
5.3 Finite-Volume Time-Domain Method . . . . . . . . . . . . . . . . . . . 133
5.3.1 Finite-Volume Formulation . . . . . . . . . . . . . . . . . . . . . 134
5.3.2 Rigid Boundary Conditions . . . . . . . . . . . . . . . . . . . . . 136
5.3.3 Computational Setup. . . . . . . . . . . . . . . . . . . . . . . . . . 136
5.3.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 138
5.3.5 Computational Loads. . . . . . . . . . . . . . . . . . . . . . . . . . 139
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
Contents ix
Part II Applications to Architectural and Environmental
Acoustic Problems
6 Room Acoustics Simlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Reiji Tomiku, Shinichi Sakamoto, Noriko Okamoto, Yosuke Yasuda,
Yoshinari Horinouchi and Kazuma Hoshi
6.1 Auditoria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
6.1.1 Application of FDTD Method. . . . . . . . . . . . . . . . . . . . 146
6.1.2 Application of FEM and BEM . . . . . . . . . . . . . . . . . . . 150
6.2 Seating Rows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
6.2.1 Analysis with Layer Model Admittance. . . . . . . . . . . . . 155
6.2.2 Analysis with Seat Top Section Admittance. . . . . . . . . . 160
6.3 Reverberation Rooms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
6.3.1 Comparison with Measurement Results . . . . . . . . . . . . . 163
6.3.2 Descriptors for Diffuseness of Sound Fields. . . . . . . . . . 164
6.4 Vehicle Cabins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
6.4.1 Boundary Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . 168
6.4.2 Numerical Analysis of Impulse Responses. . . . . . . . . . . 171
6.5 Partitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
6.5.1 Insulation Effect of Arrayed Partitions. . . . . . . . . . . . . . 174
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
7 Noise Propagation Simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Masahiro Toyoda, Takuya Oshima, Takatoshi Yokota,
Tomonao Okubo, Shinichi Sakamoto, Yosuke Yasuda,
Takashi Ishizuka, Yasuhito Kawai and Takumi Asakura
7.1 Outdoor Noise Propagation. . . . . . . . . . . . . . . . . . . . . . . . . . . 180
7.1.1 Influence of Wind. . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
7.1.2 Efficient Calculation of Long-Range Propagation. . . . . . 183
7.1.3 Chained Simulation of CFD and LEE Method . . . . . . . . 188
7.2 Noise Barriers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
7.2.1 2.5-D Analysis Using BEM . . . . . . . . . . . . . . . . . . . . . 195
7.2.2 Numerical Examples. . . . . . . . . . . . . . . . . . . . . . . . . . 196
7.2.3 Notes on Absorbing Boundaries . . . . . . . . . . . . . . . . . . 200
7.3 Depressed Roads. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
7.3.1 2-D Analysis Using FDTD Method. . . . . . . . . . . . . . . . 200
7.3.2 2.5-D Analysis Using FDTD Method . . . . . . . . . . . . . . 204
7.3.3 3-D Analysis Using FMBEM. . . . . . . . . . . . . . . . . . . . 206
7.4 Building Façades. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
7.4.1 2-D Analysis Using BEM . . . . . . . . . . . . . . . . . . . . . . 211
7.4.2 3-D Analysis Using FMBEM. . . . . . . . . . . . . . . . . . . . 217
7.5 Building Windows. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
7.5.1 Flanking Propagation Between Apertures. . . . . . . . . . . . 220
7.5.2 Propagation Through Facing Apertures . . . . . . . . . . . . . 225
x Contents
7.6 Floor Impact Sound. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
7.6.1 Solid Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
7.6.2 Plate Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
8 Acoustic Property Simulation for Building Components . . . . . . . . 243
Takumi Asakura, Yasuhito Kawai, Hisaharu Suzuki, Naohisa Inoue,
Tetsuya Sakuma, Hirofumi Onitsuka and Takayuki Masumoto
8.1 Absorbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
8.1.1 Assumption of Locally Reacting Condition . . . . . . . . . . 244
8.1.2 Area Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
8.1.3 Simple FDTD Model. . . . . . . . . . . . . . . . . . . . . . . . . . 252
8.1.4 Layered Material FE Model. . . . . . . . . . . . . . . . . . . . . 257
8.2 Diffusers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
8.2.1 BE Analysis of Surface Scattering . . . . . . . . . . . . . . . . 269
8.2.2 Calculation of Surface Scattering Indicators. . . . . . . . . . 272
8.3 Insulation of Windows. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
8.3.1 Analysis Using BEM. . . . . . . . . . . . . . . . . . . . . . . . . . 275
8.3.2 Analysis Using FDTD Method. . . . . . . . . . . . . . . . . . . 279
8.4 Acoustic Radiation from Loudspeakers . . . . . . . . . . . . . . . . . . 283
8.4.1 Calculation Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 285
8.4.2 Numerical Examples. . . . . . . . . . . . . . . . . . . . . . . . . . 287
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
9 Auralization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
Takatoshi Yokota, Takumi Asakura and Takayuki Masumoto
9.1 Room Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
9.1.1 Multichannel Reproduction System
with FDTD Method. . . . . . . . . . . . . . . . . . . . . . . . . . . 296
9.1.2 Simulation of Room Impulse Responses . . . . . . . . . . . . 297
9.1.3 Effects of Sound Diffusers in Rooms . . . . . . . . . . . . . . 299
9.1.4 Auralization of ‘‘Roaring Dragon’’ . . . . . . . . . . . . . . . . 300
9.2 Noise Propagation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
9.2.1 Auralization Method . . . . . . . . . . . . . . . . . . . . . . . . . . 303
9.2.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
9.3 Head-Related Transfer Functions. . . . . . . . . . . . . . . . . . . . . . . 308
9.3.1 Basic Examination . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
9.3.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319