Computational Acoustics of Noise Propagation in Fluids - Finite and Boundary Element Methods (eBook)

Preface 7
Contents 9
List of Contributors 11
0 A Unified Approach to Finite and Boundary Element Discretization in Linear Time - Harmonic Acoustics 14
0.1 Introduction 14
0.2 Approach to theWave Equation 15
0.3 The Boundary Value Problem 20
0.4 Discretization Process 24
0.5 Sources and Incident Wave Fields 29
0.6 Categorization of Subsequent Chapters 33
0.7 FEM and BEM for Acoustics: Future Work 35
0.8 Conclusions 41
References 42
Part I FEM: Numerical Aspects 49
1 Dispersion, Pollution, and Resolution 50
1.1 Introduction 50
1.2 Conventional Galerkin Approximation 51
1.3 Recent Developments 61
1.4 Conclusions 66
References 66
2 Different Types of Finite Elements 70
2.1 Introduction 70
2.2 Formulation of Finite Element Method for Acoustical Problems 71
2.3 Hierarchical Finite Elements for Acoustics 79
2.4 Mixed Spectral Finite Elements 86
2.5 Outlook 98
References 99
3 Multifrequency Analysis using Matrix Pade- via- Lanczos 102
3.1 Introduction 102
3.2 Pade Approximation 103
3.3 Matrix Pade-via-Lanczos 107
3.4 Application to Structural Acoustics 109
3.5 Extension to Acoustics in an Exterior Domain 114
3.6 Error Estimate and Adaptation 118
3.7 Numerical Examples 122
3.8 Conclusion 124
References 126
4 Computational Aeroacoustics based on Lighthills Acoustic Analogy 128
4.1 Introduction 128
4.2 Hybrid Approach Using Lighthills Acoustic Analogy 132
4.3 Validation of the Computational Scheme 140
4.4 Flow-induced Noise from 3D Wall Mounted Cylinders 143
4.5 Conclusion 152
References 153
Part II FEM: External Problems 156
5 Computational Absorbing Boundaries 158
5.1 Computational Absorbing Boundaries - What are they? 158
5.2 Milestones in the Development of Absorbing Boundaries and Layers 164
5.3 Concluding Remarks 176
Acknowledgment 178
References 178
6 Perfectly Matched Layers 180
6.1 Introduction 180
6.2 Time-domain Cartesian PML Equations 183
6.3 Time-harmonic Cartesian PML Equations 189
6.4 Time-harmonic Radial PML Equations 199
6.5 Further Research 206
Acknowledgments 206
References 206
7 Infinite Elements 210
7.1 Preliminaries 210
7.2 The Unbounded Helmholtz Problem 212
7.3 Infinite Elements. A One-dimensional Tutorial 213
7.4 Infinite Elements in Three Dimensions 221
7.5 Accuracy and Performance 232
7.6 Conditioning 234
7.7 Infinite Elements in the Time Domain 237
7.8 Conclusions 240
References 241
8 Efficient Infinite Elements based on Jacobi Polynomials 244
8.1 Introduction 244
8.2 Acoustic Finite and Infinite Elements 245
8.3 Preconditioners and Krylov Subspace Methods 248
8.4 Improved Astley-Leis Elements 249
8.5 Numerical Examples 254
8.6 Conclusions 260
Acknowledgments 261
References 261
Part III FEM: Related Problems 264
9 Fluid-Structure Acoustic Interaction 266
9.1 Introduction 266
9.2 Notation 268
9.3 Spectral PDE Problems in Elastoacoustics 269
9.4 Weak Formulations of the Spectral Problems 273
9.5 Finite Element Approximation 275
9.6 A Modal Synthesis Method 283
9.7 Numerical Results for Spectral Problems 285
9.8 Fluid-Structure Interaction with Interface Damping 288
9.9 A Pure Displacement Formulation for the Time Domain Problem 292
9.10 Conclusions 297
Acknowledgments 297
References 298
10 Energy Finite Element Method 300
10.1 Background and Motivation 300
10.2 Governing Equations 302
10.3 Energy Finite Element Method (EFEM) Formulations 303
10.4 Engineering Application 313
10.5 Conclusions 317
References 318
Part IV BEM: Numerical Aspects 320
11 Discretization Requirements: How many Elements per Wavelength are Necessary? 322
11.1 Introduction 322
11.2 Continuous and Discontinuous Boundary Elements 325
11.3 Error Measures 329
11.4 Computational Example: Long Duct 330
11.5 Computational Example: Sedan Cabin Compartment 339
11.6 Conclusions 342
References 343
12 Fast Solution Methods 346
12.1 Introduction 346
12.2 Iterative Solution 347
12.3 Efficient Evaluation of the Matrix-Vector Product 357
12.4 Conclusion 374
References 375
13 Multi-domain Boundary Element Method in Acoustics 380
13.1 Introduction 380
13.2 Conventional Multi-domain BEM 382
13.3 Direct Mixed-body BEM 384
13.4 Substructuring: Multi-domain BEM Revisited 389
13.5 Silencer Test Case 393
13.6 Conclusions 397
Acknowledgements 398
References 398
14 Waveguide Boundary Spectral Finite Elements 400
14.1 Introduction 400
14.2 Weak Formulation for the Spectral Finite Element 402
14.3 Wave Influence Functions & the Dynamic Stiffness Matrix
14.4 Examples for Two-dimensional Spectral Finite Elements 408
14.5 Results from a Three-dimensional Analysis 412
14.6 Conclusions 417
References 419
Part V BEM: External Problems 422
15 Treating the Phenomenon of Irregular Frequencies 424
15.1 Introduction 424
15.2 Boundary Element Formulation 426
15.3 Irregular Frequencies 428
15.4 CHIEF and its Variations 428
15.5 Superimposing First and Second Integral Equation 431
15.6 Other Methods 432
15.7 Test Cases 433
15.8 Conclusion 444
Acknowledgement 445
References 445
16 A Galerkin-type BE-formulation for Acoustic Radiation and Scattering of Structures with Arbitrary Shape 448
16.1 Introduction 448
16.2 Derivation of the Integral Equation 450
16.3 Galerkin-type Numerical Solution Scheme 459
16.4 Programming Aspects 463
16.5 Numerical Study 466
16.6 Conclusion 470
References 471
17 Acoustical Radiation and Scattering above an Impedance Plane 472
17.1 Introduction 472
17.2 Theory 473
17.3 Numerics 489
17.4 Conclusions 504
Acknowledgements 505
References 505
18 Time Domain Boundary Element Method 508
18.1 Introduction 508
18.2 Sound Wave Propagation 510
18.3 Boundary Integral Equations 513
18.4 Boundary Element formulation 518
18.5 Application 522
18.6 Conclusion 524
A Convolution Quadrature Method 527
References 528
Part VI BEM: Related Problems 530
19 Coupling a Fast Boundary Element Method with a Finite Element Formulation for Fluid - Structure Interaction 532
19.1 Introduction 532
19.2 Boundary Element Formulation for the Fluid Domain 534
19.3 Finite Element Formulation for the Structural Domain 539
19.4 Combined Interior and Exterior Acoustic Problem 541
19.5 Strong Fluid-Structure Coupling 547
19.6 Conclusion 555
Acknowledgement 555
References 556
20 Inverse Boundary Element Techniques for the Holographic Identification of Vibro - Acoustic Source Parameters 560
20.1 Introduction 560
20.2 Summary of Theoretical Background 564
20.3 Practical Application Examples 572
20.4 Perspective on the Further Works 576
20.5 Conclusions 581
Acknowledgements 581
References 582
Index 586